



































































































































































































































































* ‘ 












I 


































































































































. 






. 








■ 




















PHYSICAL 

LABORATORY EXPERIMENTS 

FOR 

ENGINEERING STUDENTS 


BY 

SAMUEL SHELDON, Ph.D., D.Sc. 

•I 

Late Professor of Physics and Electrical Engineering 
at the Polytechnic Institute of Brooklyn 

AND 

ERICH HAUSMANN, E.E., Sc.D. 

Professor of Physics and Electrical Communication 
at the Polytechnic Institute of Brooklyn 


40 ILLUSTRATIONS 


PART 1. 

MECHANICS, SOUND, HEAT, AND LIGHT 


SECOND EDITION, CORRECTED 



» » » 

NEW YORK 

D. VAN NOSTRAND COMPANY 
EIGHT WARREN STREET 
1921 








3 ^ 

S5 


Copyright, 1917 

BY 

D. VAN NOSTRAND COMPANY 


Copyright, 1921 

BY 

D. VAN NOSTRAND COMPANY 


OCT 25 1921 


§)C!.A627409 




PREFACE 


The material in thits volume was prepared for the use 
of sophomore students in the Polytechnic Institute of 
Brooklyn. All of these students are candidates for engi¬ 
neering degrees and most of them, when they entered 
as freshmen, had pursued courses in laboratory physics 
in the high schools of Greater New York, which are gener¬ 
ally supplied with superior laboratory equipments. The 
book comprises thirty exercises, and the performance of 
each is designed to occupy three hours of the student’s 
time. The course, therefore, covers three hours per week 
for two semesters. Each experiment has been chosen 
because of its close connection with engineering work, and 
in many cases the theoretical result may be calculated 
from the constants of the apparatus with which that result 
obtained by experiment may readily be compared. As 
these two results approach to an equality the student 
gains confidence in the apparatus, confidence in the theory, 
and confidence in himself. Apparatus of engineering de¬ 
sign has been chosen for each exercise so that the student 
may rely upon getting the same result under the same 
conditions, and the results obtained by different students 
are directly comparable with each other. Each exercise 
is self-contained and assumes a knowledge on the part 
of the student of the subject matter as treated in courses 
on college physics. College Physics by Reed and Guthe 
is the text used at the Polytechnic. The additional 
theory necessary for a thorough understanding of an 
exercise is suggestively given with a view to inspiring 
the student to think and to supply the gaps. 




IV 


PREFACE 


It is believed that many other teachers of laboratory 
physics to engineering students may be confronted with 
the same conditions as exist at the Polytechnic. It is 
hoped that this text may be of some service to them in 
the solution of their problems. 

S. S. 

E. H. 

Polytechnic Institute of Brooklyn, 

January, 1917. 



CONTENTS 







EXPERIMENT TITLE PAGE 

1. Radius of Curvature of Lenses by Spherometer. 1 

2. Measurement of Areas by Planimeter. 6 

3. Acceleration of Gravity by Atwood’s Machine. 11 

4. Acceleration of Gravity by Falling Body. 14 

5. Coefficient of Restitution and Hardness by Sclercscopc.... 17 

6. Moment of Inertia of Rotating Wheel. 22 

7. Study of Harmonic Motion of Rotating System. 26 

8. Stretch Modulus of Elasticity. 30 

9. Shear Modulus of Elasticity. 33 

10. Specific Viscosities of Liquids. 38 

11. Conformity of Air with Boyle’s Law. 43 

12. Specific Gravity of Gases with Effusiometer. 45 

13. Calibration Curve of Venturi Meter. 48 

14. Velocity of Sound—Specific Heats of a Gas. 50 

15. Coefficient of Expansion of Gases by Air Thermometer... 57 

16. Specific Heats of Solids. 62 

17. Heat Equivalent of Electrical Energy. 65 

18. Mechanical Equivalent of Heat. 68 

19. Heat of Fusion of Ice. 71 

20. Heats of Combustion of Fuels. 74 

21. Dew-point and Humidity of Atmosphere. 78 

22. Thermal Conductivity of Metals. 82 

23. Refractive Index of Prism. 84 

24. Focal Lengths of Convex Lenses—Radius of Curvature of 

Concave Mirror. 88 

25. Calibration of Ocular Scale of Cathetometer. .. 92 

26. Curvature of Cornea of Eye with Ophthalmometer. 94 

27. Magnifying Power of a Compound Microscope. 102 

28. Wave-lengths of Light by Interferometer. 109 

29. Wave-lengths of Light by Diffraction. 113 

SO. Photometric Test of Incandescent Lamp. 115 

Tables of Physical Constants. 123 


v 






































PHYSICAL LABORATORY 
EXPERIMENTS 


EXPERIMENT 1 

Radius of Curvature of Lenses by Spherometer 


Object. To determine the radius of curvature of a 
concave and of a convex lens with the use of a spherom¬ 
eter, a micrometer caliper, and a vernier caliper. 

Theory. The spherometer consists of a screw moving 
vertically in a nut mounted at the center of an equilateral 
tripod. The instrument is arranged to measure accu¬ 
rately the distance between the point of the screw and 
the plane of the three tripod legs. If the spherometer 
reading be a and the distance between the axes of the 
screw and tripod leg be r, it follows that the radius of a 
vertical circle which passes through the point of the screw 
and the end of one tripod leg, and whose center lies on 
the prolonged axis of the spherometer screw, is 


R = - + - 
2a ' 2’ 


The distance r can be expressed in terms of the mean 
length l between centers of the tripod legs, from the 
geometry of the equilateral triangle formed by these 
legs. Thus 

l 

V3 > 


r = 




2 


PHYSICAL LABORATORY EXPERIMENTS 


and substituting this value in the foregoing equation, then 


R = 


ii 

6a 



Apparatus. Spherometer, micrometer caliper, vernier 
caliper, plane surface, concave and convex lenses. 

Spherometer. The spherometer, Fig. 1, carries a 
graduated circular disk at the top of the screw, and a 
fixed vertical scale graduated in 
divisions equal to the pitch of 
the spherometer screw. The 
whole number of revolutions of 
the screw can be read on the 
vertical scale and the fractions 
of a turn can be read on the disk. 
To take a zero reading, place 
the instrument on a true plane 
surface and turn the screw slowly 
by means of the knurled head 
until the entire spherometer just 
begins to revolve around the 
screw point as pivot. When this 
occurs without noticeable rocking 
of the instrument on the surface, 
the reading is taken by observing the indications on the 
vertical and circular scales and adding them. The settings 
of the circular scale should be estimated to tenths of 
divisions. Readings on other surfaces are made sim¬ 
ilarly. 

Micrometer caliper. The micrometer caliper, Fig. 2, 
is based upon the same operating principle as the sphe¬ 
rometer. It consists of a screw moving in a U-shaped 
frame, the screw being provided with a hollow graduated 
head which can be turned back and forth over a fixed 
longitudinal scale. An object to be measured is placed 
between the screw and the anvil and the screw is turned 
until a slight pressure is felt. The whole turns of the 



Fig. 1. 








PHYSICAL LABORATORY EXPERIMENTS 


3 


screw are read upon the fixed scale and the fractions of a 
turn are read upon the micrometer head; together they 
indicate the thickness of the object. Calipers are fre- 



Fig. 2. 


quently provided with a ratchet head for guarding against 
the application of excessive pressure on the micrometer 
screw. 

Vernier caliper . The vernier caliper, Fig. 3, consists 



of a slider with a projecting jaw that can be moved along 
a graduated bar or scale also provided with a jaw, the 
instrument being designed to measure accurately the 
distance between these jaws by means of the scale and by 
the vernier carried on the slider. The vernier has n equal 
























4 


PHYSICAL LABORATORY EXPERIMENTS 


spaces or divisions whose aggregate length is equal to 
that of uzt 1 of the smallest divisions on the scale. There¬ 
fore the length of each vernier division is — = * = --, or 1 =L -, 

n 7i 

of the smallest scale division, that is, the vernier division 


is - of the smallest scale division more or less than such 

n 

division. This slight difference in the lengths of vernier 
and scale divisions, called the least count L of the vernier, 
enables the determination of fractional parts of divisions 
on the fixed scale with precision. In measuring the length 
of an object, the jaws of the caliper are brought into light 
contact with the object, and the scale reading up to the 
zero point or index of the vernier is observed. When 
the index does not exactly meet a mark on the scale, 
the length of the fractional scale division is determined 
by observing which vernier mark coincides exactly with 
a mark on the scale. If this coincidence occur at the <?th 
vernier mark, the length of the fractional scale division 
is evidently qL, and this amount is to be added to the 
direct scale reading. 

Procedure. Take four readings with the spherom- 
eter on each lens and on the plane surface. Measure 
the diameter of each of the cylindrical spherometer 
legs four times with the micrometer caliper. Measure 
with the vernier caliper the distances between the out¬ 
sides of every two spherometer legs four times. Prom 
these measurements and those made with the micrometer 
caliper, compute the average distance between the con¬ 
tact points of the spherometer legs. Make zero correc¬ 
tions in all instrument measurements. In making 
spherometer measurements on a convex lens after hav¬ 
ing taken the zero reading on plane glass observe that 
the spherometer screw is turned in a direction opposite 
to that of the circular scale. 

Observations. The observations should be recorded 
in tabular form as follows: 



PHYSICAL LABORATORY EXPERIMENTS 


5 


Instrument Constants 

Spherometer: 

Length of divisions on fixed scale -cm. 

Number of divisions on disk - 

Value of each disk division -cm. 

Micrometer caliper: 

Length of divisions on fixed scale — in. 

Number of divisions on micrometer head- 

Value of each division on head -in. 

Vernier caliper: 

Length of smallest scale division-- in.,-cm. 

Number of divisions on vernier - 

Least count of vernier -in.,-cm. 


Spherometer Readings (cm.) 

On plane glass On concave lens On convex lens 


Aver. 


Aver.- Aver. 

(<*)=— («o= 


Diameter of Tripod Legs (in.) 

Zero reading Leg A Leg B Leg C 


Aver.- Aver, reading on the three legs 

Mean diameter of tripod leg- in. = 


cm. 














































6 


PHYSICAL LABORATORY EXPERIMENTS 


Distance between Outsides of Tripod Legs {cm.) 


Zero reading 


Leg A to 
Leg B 


Leg B to 
Leg C 


Leg A to 
Leg C 


Aver.- Average distanc 5 - 

Mean distance between outsides of tripod legs -. 

Mean distance between centers of tripod legs {l) -. 

Conclusions. Calculate the radii of curvature of 
the lenses from the foregoing equations. 


EXPERIMENT 2 

Measurement cf Areas by Planimeter 

Object. To determine the areas of several irregular 
plane figures by means of the Amsler planimeter. The 
figures to be measured are: a current-time curve, a 
hysteresis loop, a railway speed-time curve, and an indi¬ 
cator diagram; these are given on the accompanying 
detachable sheet. 

Theory. The planimeter, Fig. 4, is an instrument con¬ 
sisting essentially of a beam which carries a tracing 
point or stylus at one end and a graduated wheel with a 
smooth protruding rim near the other end, the axis of the 
wheel being parallel to the beam. An auxiliary arm is 
hinged to the beam at some convenient point, while 
the other end of this arm carries a needle point. The 
instrument, when placed upon a horizontal surface, rests 
upon the needle point, the stylus and the periphery of 
the wheel. To measure the area of a closed plane figure 
drawn on smooth paper, the stylus is carefully moved 
once around the perimeter of the figure, while the needle 






















PRESSURE 

SCALE: HN.= 48LB.PER 
SQ. IN. 



Hysteresis Loop. 



VOLUME 

Indicator Diagram. 















? 




1 










































! 






_ 




























I 















MILES PER HOUR 

















































































PHYSICAL LABORATORY EXPERIMENTS 


7 


point maintains a fixed position by being pressed into the 
paper. During this movement the wheel rotates and 
slides; the rotatory motion results from a movement 
of the beam in a direction perpendicular to itself, and 
the sliding motion results from a movement of the beam 
along its own direction. The net rotation of the wheel 
for one complete transit of the stylus along the perimeter 
of a figure indicates the area of that figure directly, when 
the needle point is fixed outside of that area. 

In Fig. 5, let AB be the planimeter beam of length l , 
AN be the auxiliary arm with its needle point fixed at N f 



Fig. 4. 

and W be the position of the wheel which is located a 
distance d from the center point of AB. Consider the 
motion of the beam while the stylus B moves a very 
small distance BB'" along the perimeter of the figure 
whose area S is to be measured, this distance being 
greatly exaggerated in the figure for the sake of clearness. 
The movement of the beam from AB to A'" B'" may be 
resolved into three simple component movements, as 
follows: 1, a motion of rotation about W to the posi¬ 
tion A'B'; 2, a motion of translation perpendicularly 
to itself to the position A"B"; and 3, a motion of trans¬ 
lation along itself to the position A"'B'", the auxiliary 
arm being considered detached during these movements. 



8 


PHYSICAL LABORATORY EXPERIMENTS 


Areas are swept out by the beam during the first and 
second of these component movements, and when such 
areas are swept out toward the right they are considered 
positive, and toward the left negative. The net area 
of rotation of the beam through the angle 6 is equal to 
the area of the sector BB'W minus the area of the sector 
AA'W, which can be shown to be equal to Old. The 
distance s through which the beam moves perpendicularly 
to itself is best measured by noting the angular movement 
of the wheel in moving from W to w. The diagram in 



the upper corner of Fig. 5 shows that the wheel of radius 
r turns through the angle </> in order for the wheel to 
move from W to w; therefore s = r</>. The area of the 
rectangle A'A"B"B' which is swept out by translation 
is equal to lr(f>. Consequently the total area swept 
out by the beam when the stylus traverses the elemen¬ 
tary portion BB"' of the perimeter of the figure is 
Bid + When the stylus moves once completely 

around the perimeter of the closed figure in a clockwise 
direction, any area outside of the figure which is swept 
over by the beam is swept out once toward the right and 
once toward the left, while the area of the figure itself is 




PHYSICAL LABORATORY 7 EXPERIMENTS 


9 


swept out only toward the right, therefore the area of the 
figure is 

S = 2 Old + 2Zr0. 

Since the beam resumes its original position after a 
complete transit of the stylus, 20 = 0, whence 

S = fr20, 

where 20 is the net rotation of the wheel during one 
complete transit of the perimeter by the stylus. It is 
evident from this equation that the periphery of the 
wheel of a planimeter may be graduated to read directly 
in units of area. 

When the area that is to be measured is very large, 
it is convenient to place the needle point inside of the 
area. The planimeter reading taken after one complete 
transit of the perimeter is less than the area of the figure. 
The true area is obtained by adding to the planimeter 
reading (with attention to sign) the area of a datum circle 
which is generated by the stylus when it moves about the 
needle point as center so that the wheel will not rotate. 
(For proof, see p. 59 of Ferry and Jones, “ Practical 
Physics ”)• 

Apparatus. Planimeters of different makes, drawing 
boards, triangle, micrometer caliper, and scale. 

Procedure. Measure with the scale the length of 
one planimeter beam, l, from the stylus to the point 
of attachment of the auxiliary arm. In some instru¬ 
ments, Fig. 4, this distance may be readily measured 
from point to point of the upwardly projecting pins 
on the beam. Measure the diameter, 2 r, of the wheel 
over its rim with the micrometer caliper. Show that the 
area represented by one revolution of the wheel is 

Draw a rectangle having an area of from 5 to 10 square 
inches, and measure its area by a planimeter four times 
and compare the average value with the product of the 
two dimensions of the rectangle as measured with the 
scale. 

To use the planimeter, place the needle point at a 


10 PHYSICAL LABORATORY EXPERIMENTS 


convenient spot outside of the area to be measured. 
Hold the stylus at any convenient starting point, set the 
graduated wheel to its zero position against the index of 
the vernier, and then trace the perimeter of the figure 
in a clockwise direction with the stylus until the start¬ 
ing point is again reached. Read the new position 
of the wheel with the aid of the vernier. Take four 
readings on each figure with one planimeter. 

Measure the areas of the current-time curve, hyster¬ 
esis loop, speed-time curve, and indicator diagram, each 
four times, in square inches, with one of the planimeters. 
If the beam of the planimeter is of adjustable length, 
set it to read square inches. 

Observations. Record observations as below: 

Planimeter Constants 


Name of Make: Ashcroft, Dietzgen, 

or Crosby 

Length of beam 

(0 =- 

-in. 

Diameter of wheel 

(2 r) = - 

-in. 

Area per revolution of wheel 
Highest reading on wheel 

2irlr = - 

-sq. in. 

-sq. in. 

Percentage difference 

Value of smallest wheel division 


-sq. in. 

Least count of vernier 


-sq. in. 


Readings on Rectangle 

Planimeter readings (sq. in.) Length of rectangle-in. 

- - Height of rectangle-in. 

Aver. - Calculated area --sq. in 

Percentage difference-- 

Area Measurements on Irregular Figures (sq. in.) 
Current curve Hysteresis Speed-time Indicator 
loop curve diagram 


Aver.- 






























PHYSICAL LABORATORY EXPERIMENTS 


11 


Conclusions. Reduce the areas of the irregular 
figures to their proper units as indicated by their ordinates 
and abscissas, and determine their average heights. 
Explain the method of reduction and record results as 
follows: 


Figure 

Current curve 
Hysteresis loop 

Speed-time curve 
Indicator diagram 


Area Average height. 

-coulombs -amperes 

-gilbert-max¬ 
wells per cu. cm. 

-miles -miles per hr. 

-lbs. per sq. in. 


EXPERIMENT 3 

Acceleration of Gravity by Atwood’s Machine 

Object. To verify the laws of uniformly accelerated 
motion and to determine the acceleration of gravity by 
means of Atwood’s machine. 

Theory. Atwood’s machine is used to measure the 
velocity and acceleration of bodies by observing the 
spaces that are traversed by them during known inter¬ 
vals of time. For convenience, two bodies of equal mass 
are affixed to the ends of a thin cord which is hung over 
a light freely moving wheel, and the acceleration is 
produced by the force of gravity acting on a supple¬ 
mentary mass added to one of the bodies. In verifying 
the laws of uniformly accelerated motion, the expressions 
used are 

s = \at 2 , 

and _ 

v — V 2 as , 

where s is the distance traveled from rest in t seconds by 
a body moving with uniform acceleration a , and v is the 
velocity of the body acquired after moving a distance s. 

If a small weight of mass m be placed upon one of the 






12 PHYSICAL LABORATORY EXPERIMENTS 


two equal bodies, the force of gravity imparts to the total 
mass an acceleration 

mg 

a ~ M + TO ’ 

where g is the acceleration of gravity and M is the aggre¬ 
gate mass of the two bodies. By eliminating a from the 
foregoing equations, an expression for the acceleration 
of gravity may be obtained. Inasmuch as the wheel 
itself has also been accelerated, its equivalent mass 
should be added to M + m. This equivalent mass is 
equal to its moment of inertia I divided by the square of 
the distance r from its center to the cord. Introducing 
this factor, the final equation for the acceleration of grav¬ 
ity becomes 

g = 5( K+ m+ S)- 

Apparatus. Atwood’s machine, metronome, stop¬ 
watch, balance with weights, and meter-stick. 

The Atwood’s machine comprises a light pulley sup¬ 
ported at the top of a frame, two cylindrical bodies of 
equal mass attached to the ends of a cord which passes 
over the wheel, a metal rider to serve as the accelerating 
weight, a platform for arresting the motion of the de¬ 
scending body, and a ring stage for removing the rider 
from the body at particular instants during its descent. 

To take an observation, level the instrument, place the 
cylindrical bodies with the attached cord in position, 
put the rider or other weights on the rear body, and draw 
the front body to its lowest position. Start the metro¬ 
nome and exactly on a click of this device release the front 
body. The platform should then be raised or lowered 
after each trial until in its final adjustment the descending 
rear body will strike it simultaneously with a metronome 
click. When the accelerating force is to act only during 
a part of the descent, the ring stage is first adjusted to 
remove the rider exactly on a metronome click, and then 



PHYSICAL LABORATORY EXPERIMENTS 13 

the platform is adjusted at a lower position to stop the 
motion exactly on another click. The moment of iner¬ 
tia of the wheel is 150 gram-cm. 2 , and its radius is 5.1 cm. 

Procedure. Determine the weight in grams of the 
rider and of the two bodies with string. Set the metro¬ 
nome weight so that its upper edge indicates 120, and then 
count the number of clicks made in two minutes. From 
this count derive the time interval in seconds between two 
successive clicks. 

To verify the laws of accelerated motion, (a) With the 
rider on the rear body, measure with a meter-stick the 
spaces through which it moves during 2, 3 and 4 inter¬ 
vals between metronome clicks and show that these 
spaces are to each other as are the squares of the respec¬ 
tive times of descent. ( h ) Allow the rider to act only for 
2 intervals between clicks and measure the distance 
traversed subsequently during 2, 3 and 4 such intervals 
to show that the descending body travels with constant 
velocity after removal of rider, (c) Allow the rider to 
act for 1, 2 and 3 intervals between clicks and measure 
in each case the distance traversed during two such inter¬ 
vals after removal of the rider, in order to show that 
velocities acquired by the descending body while acceler¬ 
ating are directly proportional to the times of descent. 
Measure all distances to the nearest millimeter. 

To determine the acceleration of gravity. Place weights 
of 10, 20, 30, 40 and 50 grams successively on the rear 
body and measure the distances it traverses while descend¬ 
ing to the platform in some integral number of intervals 
between metronome clicks, selecting that number which 
gives the largest descent on the machine. Verify the 
position of the platform by repeated trials for each added 
weight. 

Observations and Conclusions. Record all observa¬ 
tions and arrange them in tabular form, and verify the 
laws of uniformly accelerated motion as already indicated. 
In the determination of the acceleration of gravity 
calculate the acceleration of the descending body by means 


14 PHYSICAL LABORATORY EXPERIMENTS 


of a = 2 s/t 2 , and plot a curve with a as ordinates against 
added masses on descending body as abscissas. The 
points will lie approximately in a straight line, and such 
a line is to be drawn which will pass as nearly as possible 
through all of the observational points. The intercept 
of this line on the axis of abscissas indicates that part 
of the added masses which is required to overcome fric¬ 
tion in the wheel. In the calculations this intercept 
should be subtracted from the added masses in order to 
obtain m. Calculate for each value of ra, the accelera¬ 
tion of gravity in cm. per sec. per sec., and compare the 
average value for g as obtained by test with the theoretical 
value as given in Tables II and IX. 

EXPERIMENT 4 

Acceleration of Gravity by Falling Body 

Object. To determine the acceleration of gravity by 
means of a body falling freely under the force of gravity 
before a vibrating tuning fork. 

Theory. A stylus on a vibrating tuning fork of known 
frequency / is adjusted to trace a sinuous line on the 
falling body. The distances between crests of this line 
will be found to increase as the body descends because 
of its acceleration. Mark a transverse line near the be¬ 
ginning of the trace where the curves are perfectly formed, 
and from this line mark off spaces by similar transverse 
lines, each space containing exactly 10 wave-lengths. 
Call these spaces si, S 2 , etc. Since the body had acquired 
some velocity v 0 upon reaching the first mark, it follows 

that the successive spaces described in the time — = t 

seconds, which corresponds to 10 vibrations of the fork, 
are 

51 = Vo t + \gt 2 , 

5 2 = vot + f gt 2 , 

5 3 = vot + f gt 2 , etc., 




PHYSICAL LABORATORY EXPERIMENTS 15 



Fig. 6. 













16 PHYSICAL LABORATORY EXPERIMENTS 


where g is the acceleration of gravity. Then, if S cm. 
be the mean space increment, that is, the average value 
of S 2 — si, S 3 — S 2 , etc., the acceleration of gravity in 
cm. per sec. per sec. will be 

g = r 

Apparatus. Falling-plate device with electrically 
operated tuning fork, glass or metal plate, battery, 
scale and scriber. 

The device employed in this measurement consists of 
a vertical metal frame in which slides a metal carrier 
holding a piece of plate glass, Fig. 6 . The glass plate 
is painted with a thin paste of whiting mixed with alcohol, 
and when dry is clamped to the carrier by means of two 
spring hooks. This carrier is raised and should be fas¬ 
tened at the top of the frame by a string which is passed 
through the hole in the cross-bar and fastened by being 
wrapped around a screwhead in the cross-bar. On the 
frame is mounted an electrically operated tuning fork 
which has a stylus on one prong. To take an observation, 
close the electrical circuit of the tuning fork and start 
the fork vibrating, adjusting the contact screw if neces¬ 
sary. Turn the milled screw on the tuning-fork holder 
until the stylus bears properly upon the glass, and then 
burn the string by applying a lighted match above the 
cross-bar. The descending plate will receive a fine tracing 
on its whitened surface. 

Procedure. Level the instrument so that the carrier 
may fall freely with the least amount of friction, and 
take an observation as outlined. Displace the fork 
about % inch in a horizontal direction and take another 
observation. Several trials may be necessary to yield 
good results. When two good traces have been obtained, 
remove the glass plate and rule a transverse mark upon 
every tenth crest of each trace with a scriber and scale. 
Measure the distance between successive transverse 
marks to hundredths of an inch. 


PHYSICAL LABORATORY EXPERIMENTS 17 


Observations. Denote the distances between the 
transverse marks by Si, S 2 , etc., beginning at the end of 
the trace where the wave-lengths are short, and record 
the measurements as below: 


Trace Measurements (in.) 


, . 10 

Distances traversed m — = t sec. 


Trace 1 


Trace 2 


Differences between successive 
distances 

Trace 1 Trace 2 


si 

52 

53 

54 

55 


52- S1 = - - 

53- S2 = -- - 

_ _ S4-S3 = - -- 

S5-S4 =- 

Mean space increment S = -in. =-cm. 


Conclusions. The differences between the successive 
distances $ 1 , S2, etc., should all be equal, since the accelera¬ 
tion of gravity is constant. The rate of vibration of the 
tuning fork is 285 per second, therefore the time inter¬ 
val t = - 0.03509 second. Compute the value of 

the acceleration of gravity in cm. per sec. per sec. and 
compare this value with the theoretical value at the place 
where the experiment is performed, see Tables II and IX. 


EXPERIMENT 5 

Coefficient of Restitution and Hardness by Scleroscope 

Object. To determine the coefficient of restitution and 
the relative hardness of metals by means of a Shore 
scleroscope. 

Theory. That number by which the relative velocity 
of two colliding bodies just before impact must be mul¬ 
tiplied in order to give their relative velocity just after 
impact is called the coefficient of restitution of the bodies. 
If one of the bodies be clamped stationary, then the co¬ 
efficient of restitution is the ratio of the velocities of the 











18 PHYSICAL LABORATORY EXPERIMENTS 



Fig. 7. 









PHYSICAL LABORATORY EXPERIMENTS 19 


other body just after and just before impact. In the 
scleroscope, a miniature diamond-pointed hammer is 
allowed to fall freely from a known constant height h\ 
upon the specimen under test, which is held stationary. 
If the velocity of the hammer at the instant of striking 
the specimen be Vi, its velocity just after impact be V 2 , 
and the height to which the hammer rebounds be A 2 , 
then it follows from the law of falling bodies that the 
coefficient of restitution is 



The rebound can serve directly as a measure of the 
hardness of a specimen on an arbitrary scale. The scale 
on the Shore scleroscope has 140 equal divisions, and on 
this scale hard steel corresponds to a rebound of 100. 
Then, if the hammer rebounds from a test piece to division 
55 on this scale, the piece is said to be “ 55 hard.” It is 
interesting to note that the ultimate tensile strength of 
a material is quite closely related to its hardness as 
measured by the scleroscope. 

In the instrument used in this experiment the hammer 
falls from a height of 9.90 inches, and each division of the 
scleroscope scale measures 0.0643 inch; therefore 

7c = 0.0806Vd, 

where d is the hardness or the number of divisions rebound. 

Apparatus. Scleroscope with universal hammer, 
magnifier hammer, five steel specimens of the same car¬ 
bon content but quenched at different temperatures, and 
soft metal specimens of copper, brass and bronze. 

The principal feature of the scleroscope is a small 
diamond-pointed hammer of about 40 grains mass which 
falls within a glass tube onto the metal specimens clamped 
at the base, Fig. 7. The hammer is raised to the top 
of the instrument by suction and it is released by an 
ingenious pneumatically operated mechanism, shown in 


20 PHYSICAL LABORATORY EXPERIMENTS 


Fig. 8. A hand bulb connected to tube A acts on timer 
cam B through the medium of the piston C, the adjustable 
oscillator D and the end ratchets E. When the bulb is 
pressed the cam acts on the valve F, unseating it, and 
shortly thereafter the hammer G is released from the 
hook prongs H because of the downward movement of 
the hollow cone I. During the descent of the hammer 



Fig. 8. 

there will be free access of air to the glass tube. When 
the bulb is again pressed the cam seats valve F, and the 
tube chamber is placed in direct communication with the 
bulb, so that when the bulb is subsequently released 
the reduction in pressure in the tube causes the hammer 
to be drawn up and caught on the hook prongs. 

Before taking an observation, turn the leveling screws 






























PHYSICAL LABORATORY EXPERIMENTS 21 

in the base until the instrument is level, as indicated by 
the bob-rod alongside of the tube barrel. Press the bulb 
and then release it quickly so as to raise the hammer to 
its clutch at the top of the tube. To take an observation 
on a flat specimen, raise the clamping shoe by the lever 
at the rear, insert the specimen, bring down the clamp¬ 
ing shoe, and hold it firmly in this position while making 
the test. Press the bulb to release the hammer and note 
quickly its height of rebound, the top of the hammer 
serving as the indicator. A preliminary reading viewed 
at a little distance will enable one to properly locate the 
magnifying glass on the scale for the final readings. 
Never allow the hammer to drop without striking some 
clamped object under it, for otherwise it is likely to break 
the glass. For greater accuracy in measuring the hard¬ 
ness of soft metals a “ magnifier hammer ” replaces the 
diamond-pointed hammer. 

Procedure. The five samples of steel to be tested 
have the same percentage of carbon content, but were 
subjected to different heat treatments. The temper¬ 
atures in degrees Fahrenheit at which these samples 
were quenched in the process of hardening are stamped 
on their ends. Take two readings at different spots 
on each steel specimen. 

Remove the standard or universal hammer under the 
direction of the laboratory instructor and substitute the 
magnifier hammer, which gives rebounds 1.78 times as 
great as the universal hammer for otherwise identical 
conditions. Take two readings on copper, on brass, and 
on phosphor bronze with the magnifier hammer and 
reduce these readings to the standard scale. 

Observations and Conclusions. Arrange data m 
tabular form and determine the hardness and coefficient 
of restitution of each sample tested. Compare the 
hardness values obtained by test with the values given 
in Table III. For the steel samples plot curves of hard¬ 
ness and of coefficients of restitution as ordinates against 
quenching temperatures as abscissas. 


"22 PHYSICAL LABORATORY EXPERIMENTS 


EXPERIMENT 6 

Moment of Inertia of Rotating Wheel 

Object. To determine the moment of inertia of a 
cylindrical wheel by measuring its acceleration when 
subject to a known torque and by calculation from its 
mass and dimensions. 

Theory. Consider an annular element of radius r 
and of width dr, within a cylinder of outside radius R, 
of axial length l, and of density <5. The mass of this 
element is 

dm = 2irrl8dr. 

If a torque dT acts on this element, its particles will 
acquire the linear acceleration a and the angular accelera¬ 
tion a ; whence 

dT = ardm = ar 2 dm = 2 tt l8ar 3 dr. 

By integration, the total torque acting on the entire 
cylinder becomes 


T= ^ ISaR 4 = \MR 2 a, 

since the total mass of the cylinder M=ttR 2 18. The 
portion \MR 2 is a constant of the cylinder called its 
moment of inertia, and if this constant be represented 
by /, the expression for the constant torque becomes 

T = Ia. 

The angular acceleration is measured as in Experiment 
4 by allowing a stylus on a vibrating tuning fork of known 
frequency to trace a sinuous line on the periphery of the 
wheel, and by measuring the angular distances moved 
through in equal intervals of time. If the angles sub- 


PHYSICAL LABORATORY EXPERIMENTS 23 


tended by successive groups, each of 50 wavelengths, 
be denoted by 0 1 , 02 , 03 , etc., then 

0i = wo t + \at 2 , 

02 = coo t + | at 2 , 

03 = wo£ + fotf 2 , etc., 

where coo is the angular velocity of the wheel upon reach¬ 
ing the beginning of the first group of waves, and t is the 
common time corresponding to 50 complete vibrations 
of the tuning fork. From these equations it is evident 
that the angular acceleration a is the average of 



03 -■ 02 

~1T~ 


etc. 


Apparatus. Heavy pivoted wheel with electrically 
operated tuning fork, battery, accelerating weight, 
friction-balance weight, try-square, scale, caliper, and 
scriber. 

The wheel is mounted as shown in Fig. 9 so as to re¬ 
volve about a horizontal axis. The constant torque to 
be applied in order to revolve the wheel with uniformly 
accelerated motion is obtained by a weight attached 
to a cord which passes around the small cylindrical pro¬ 
jection on the side of the wheel. The tuning fork is 
mounted on a carriage which can be moved in a direc¬ 
tion parallel to the axis of the wheel, so that the stylus 
on the fork may trace out a sinuous line extending over 
several revolutions of the wheel without overlapping. 
One side of the wheel is graduated in degrees. 

Procedure. Coat the rim of the wheel with a mix¬ 
ture of whiting and alcohol, attach one end of a string to 
the projection on the wheel with a small amount of wax 
and place the friction-balance weight and an accelerat¬ 
ing weight of 200 grams on the other end of the string. 
Wind up the string and close the circuit of the tuning- 
fork magnet. Adjust the stylus by means of the knurled 



24 PHYSICAL LABORATORY EXPERIMENTS 


screw on the carriage until it bears properly upon the 
wheel and then release the wheel. As the wheel revolves, 
slowly move the fork by means of the lever at its base 
so that the stylus travels axially across the whitened 



Fig. 9. 

surface. A moment before the descending weight reaches 
the floor either stop the rotation of the wheel, or stop the 
vibration of the tuning fork. 

When a good trace has been obtained on the wheel 
place a transverse mark with the aid of a scriber and 
try-square upon every fiftieth wave crest until 10 groups 






PHYSICAL LABORATORY EXPERIMENTS 25 


of 50 vibrations have been counted. By means of the try- 
square determine the angular position of each transverse 
mark, reading to the nearest tenth of a degree. The rate of 
vibration of the fork is 128 per second, and therefore the time 
required to describe a group of vibrations is / = t 5 2°8 second. 

With the calipers and scale measure in cm. the dimen¬ 
sions of the wheel and its cylindrical projection. The 
rotating wheel may be considered as composed of two 
disks placed side by side, their aggregate mass being 
11,340 grams. Letting M\ be the mass of the large 
disk of radius Ufa, and M 2 be the mass of the small disk of 
radius R 2 , then the moment of inertia of the wheel by 
calculation from the measured dimensions is 

I = %(MiRi 2 + M 2 R 2 2 ) gram-cm. 2 

Observations and Conclusions. ■ Record the angular 
position in degrees of each transverse mark for the 10 
groups of vibrations. Derive from these readings the 
angular distance subtended by each group, and also the 
angular distance gained by each group over the next 
preceding one. Arrange these values in parallel columns. 
Compute the average angular gain in second, convert 
to radians, and deduce the angular acceleration a in radi¬ 
ans per sec. per sec. Calculate the torque acting on the 
wheel from T = 200 R 2 (g — aife) dyne-cm., in which 
the factor 200 a R 2 is the part of the impressed force 
which is necessary to accelerate the descending 200- 
gram weight. Finally compute the moment of inertia 
of the wheel in gram-cm. 2 

Record the radius and axial length of the two disks 
which form the wheel, and calculate their volumes sep¬ 
arately. Apportion the total mass of the wheel between 
the two disks, ignoring the hole for the shaft, and then 
compute the moment of inertia of the wheel from its 
mass and dimensions. Compare the results obtained by 
the two methods. 


26 PHYSICAL LABORATORY EXPERIMENTS 


EXPERIMENT 7 

Study of Harmonic Motion of Rotating System 

Object. To determine the moment of inertia of a 
body executing harmonic rotatory motion and to ascer¬ 
tain the influence on the vibration period of increasing 
its moment of inertia by the addition of weights. 

Theory. Consider a body, capable of rotatory vibra¬ 
tion about some axis without friction, to be displaced 
from its position of equilibrium by an angle <L, and then 
released. The resulting motion of the body will be 
simple harmonic and its displacement from the equilib¬ 
rium position t seconds after being released will be 

, , 27 rt 

<{> = 4 > COS ~y , 


where T is the time of one complete vibration. Its 
angular acceleration at that instant will be 


_ d 2 <f) 47r 2 2i rt 4 t 2 

~ dt 2 ~ ~ T 2 ^ C0S ~T ~ ~ ~T 2 * ’ 


which shows that the angular acceleration of the body 
varies directly as the angle of displacement and is directed 
toward the position of equilibrium. If the moment of 
inertia of the body be I, the torque acting on it to return 
the body to its equilibrium position will be 




The factor 4tt 2 // T 2 is a constant, say b, for a given body 
executing rotatory harmonic motion, and from the fore¬ 
going equation may be defined as the torque per unit 
angle (radian) of deflection or twist. This constant b 
is readily obtained experimentally by applying a mass 


PHYSICAL LABORATORY EXPERIMENTS 27 


m subject to gravitational force at a distance r from the 
axis of rotation and noting the angle of twist </> when 
the body comes to rest; then 



where g is the acceleration of gravity. Should another 
body of moment of inertia /' be added to the vibrating 
body, its period of oscillation will be altered and assume 
the new value 

f¥- 

Apparatus. Rotatory harmonic motion apparatus 
with small weights, two cylindrical masses, balance with 
weights, stop-watch, calipers, and scale. 

The rotatory harmonic motion apparatus, Fig. 10, 
consists essentially of a pivoted body carrying a pointer 
that moves over a circular scale, which body is attached 
to one end of a flat spiral spring whose other end is fixed 
to the supporting frame. A small horizontal wheel of 
radius r is fastened near the top of the pivoted body, and 
a cord attached to this wheel extends over a vertical 
pulley to a scale pan. By placing weights on this pan and 
observing the corresponding angular displacements of 
the body, the calculation of the rotational constant b is 
made possible. When the body is displaced from its 
position, of equilibrium and released, it oscillates to and 
fro harmonically. While the motion is damped by 
friction, the period of oscillation (i.e., the time of one 
complete oscillation) is inappreciably affected thereby. 

Procedure. To determine the rotational constant, 
apply a small weight in grams to the scale pan and 
measure the angle of displacement in degrees. Be care¬ 
ful to compensate for static friction. Then apply another 
weight of known mass to the first one, and measure the 
total angle of displacement. Repeat this process by 





28 PHYSICAL LABORATORY EXPERIMENTS 


adding successively three other weights. Measure with 
the calipers the radius of the wheel which is attached to 
the pivoted body. 

To measure the period of vibration of the pivoted body, 



Fig. io. 

place tne scaie pan and cord in such position as not to 
interfere with its free vibration and determine with a stop¬ 
watch the time required in making ten complete vibra¬ 
tions. Repeat this measurement three times. 









PHYSICAL LABORATORY EXPERIMENTS 29 


To ascertain the influence on the period of vibration of 
increasing the moment of inertia of the pivoted body, 
clamp the two cylindrical equal masses on the extremities 
of the horizontal rod of the body at equal distances from 
the axis, and determine the time required in making ten 
complete vibrations. Repeat this measurement three 
times. 

Weigh the hollow cylinders and call their aggregate 
mass M grams. Measure in cm. the outside diameter 
D, the inside diameter d, and the axial length l of the 
cylinders. Then if R cm. be the distance from the center 
of either mass to the axis, the moment of inertia of the 
two masses about the axis of oscillation will be 

T , _ _ (D 2 + d 2 . I 2 . d2 \ 2 

r = M (—~-h + R ) gram-cm. 2 

Observations and Conclusions. Record all neces¬ 
sary data and arrange them in tabular form. Convert 
the angular displacements of the pivoted body with 
applied torque from degrees to radians. Compute the 
value of the rotational constant, b dyne-cm. per radian, 
for each displacement 0, and obtain its average value. 
From the times of 10 vibrations of the pivoted body 
both with and without the cylindrical masses, deduce 
the average periods of vibration in seconds. Calculate 
the moment of inertia I of the pivoted body from the 
period and rotational constant. Compute the total 
moment of inertia I' of the two cylinders from their 
measured dimensions and masses. Show that the ob¬ 
served period of vibration of the body with the cylinders 
attached agrees with the value calculated from the 
equation for T\. What error would be introduced in 
the calculated value for this period by assuming the 
moment of inertia of the cylinders to be I' = MR 2 gram- 
cm. 2 ? 



30 PHYSICAL LABORATORY EXPERIMENTS 


EXPERIMENT 8 
Stretch Modulus of Elasticity 

Object. To verify Hooke’s law and to determine the 
stretch or Young’s modulus of elasticity of various metals. 

Theory. Hooke’s law states that when an elastic 
body is subject to a stress below its elastic limit, that 
body is strained to an amount always proportional to 
the stress. Assume a metal rod of length L to change 



Fig. 11. 


its length by l units upon the application of a force F 
to one end of the rod of area a. Calling the ratio of the 
stress to the strain the modulus of elasticity, the stretch 
modulus for the rod under longitudinal stress may be 
expressed as 

M = s ^ ress _ ^ 
strain cl’ 

If L and l are measured in inches, a in square inches, 
and F in pounds, then the modulus is expressed in pounds 
per square inch. 

Apparatus. Single-lever testing machine, Ewing 
microscope extensometer, micrometer caliper, and rods 






















PHYSICAL LABORATORY EXPERIMENTS 31 


of machine steel, Bessemer steel, wrought iron, phosphor 
bronze and brass. 

The testing machine, Fig. 11, comprises a counter¬ 
balanced lever pivoted on a knife-edge at the top of a 
massive support. Near this pivot, the lever carries a 
block, suspended on another knife-edge, to which the 
upper end of the rod under test is attached, its lower 



end being held in the base. The other end of the 
lever carries a scale pan adapted to hold weights up to 
120 pounds. The lever ratio being 22.4, the stress or 
force per unit area on a rod of diameter D is 


F 4 IT 

a = 22 ' 4 ^’ 


where W is the weight on the scale pan. 

Fig. 12 shows the extensometer for measuring the in- 











32 PHYSICAL LABORATORY EXPERIMENTS 


crease of length of specimens under tensile tests. The 
instrument measures the extension of the rod A that 
occurs between the two pairs of opposed pointed screws 
at B and C, which, before the slotted bar at the rear 
of the extensometer was removed, were exactly 8 inches 
apart. When the rod is stressed, the left-hand pillar 
remains of constant length due to a spring at P, while 
the right-hand rod R, being held up against the frame 
Q by a spring, moves upward relative to the telescope. 
This telescope is focused on a small wire carried at the 
lower end of rod R, and the extension is observed by 
noting the number of small divisions d on the eye-piece 
scale through which the top of the cross-wire moves. 
Since each small scale division corresponds to an exten¬ 
sion of 0.0002 inch in the 8-inch length under test, the 
longitudinal strain is 


l _ 0.0002d 
L 8 * 

♦ 

The screw shown at E in Fig. 12 serves to bring the sighted 
wire to a convenient reference point on the scale. 

Procedure. Measure the diameter in inches of two 
rods at several places along their lengths with a microm¬ 
eter caliper. Clamp one rod in the testing machine, 
carefully affix the extensometer to the rod, and then 
remove the slotted bar from the extensometer. Adjust 
the position of the mirror back of the cross-wire so that 
the eye-piece scale will be well illuminated. Focus 
the eye-piece upon the ocular scale by moving the eye¬ 
piece in or out of its tube while looking through the 
telescope. Then turn the small knurled screw below 
the telescope until a sharp focus of the upper edge of the 
cross-wire is obtained. To verify correctness of this 
adjustment, move the eye vertically while looking through 
the telescope and note if parallax is present, that is, if 
a relative movement of scale and cross-wire is discernible. 
If parallax is present, repeat the adjustments of the 



PHYSICAL LABORATORY EXPERIMENTS 33 


telescope until correct. Turn screw E until the reading 
with no weights on the scale pan assumes a convenient 
value; then record this no-load reading. Place 20 pounds 
on the scale pan and take a telescope reading, estimating 
tenths of small divisions. Increase the load in steps of 
10 pounds up to 100 pounds and observe the correspond¬ 
ing extensions, checking the no-load reading frequently. 
Remove weights, extensometer and rod and then repeat 
the foregoing procedure for another metal rod. 

Observations and Conclusions. For each sample 
record the material of the rod and its diameter. Place 
the load readings and derived values in columns bearing 
the following captions: Pounds load W, extensometer 
reading (in terms of small divisions), stress in pounds 
per square inch, strain in inches per inch, and elasticity 
in pounds per square inch, M. Calculate the average 
modulus of elasticity for each rod tested, by using for the 
stress the sum of the values in the stress column and for 
the strain the sum of the values in the strain column. 
Compare results with the values given in Table IV. 
Plot curve for one rod only with stress as abscissas and 
strain as ordinates. Explain the shape of this curve. 


EXPERIMENT 9 
Shear Modulus of Elasticity 

Object. To determine the shear modulus of elasticity 
(or coefficient of rigidity) of two metal rods by noting 
the angular displacement produced by the application 
of a constant torque. 

Theory. The shear (or slide) modulus of elasticity 
is the ratio of the shearing stress S to the angle of shear <£; 
that is, the shear modulus is expressed as 

S 


34 PHYSICAL LABORATORY EXPERIMENTS 


In the case of a rectangular parallelopiped, Fig. 13 
having a horizontal face area a and a height b, and sub¬ 
jected to a shearing force F, the shearing stress is 
F 

S = -, and the strain is the distortion s divided by the 
a 

height b. But 7 is the tangent of an angle <£, which is 
b 



termed the angle of shear; and since this angle is usually 
small it is customary to write <f> = ^. Therefore the shear 
modulus of elasticity for the parallelopiped becomes 

Fb 
n = —. 
as 

To apply the foregoing to a cylindrical rod subject 
to torsional deformation, consider a hollow cylindrical 
element of radius r and of thickness dr within the solid 
cylinder of radius R and length Z, Fig. 14. With one 
end of this element clamped, the application of a torque 
dT upon the other end will cause lines such as AS, which 
were originally parallel to the axis of the cylinder, to 
assume other positions such as AB', making angles </> 
with their former positions. If the angular displace¬ 
ment of the free end be 6, then since <£ is small, the angle 
of shear becomes 















PHYSICAL LABORATORY EXPERIMENTS 35 


The shearing stress, or tangential force per unit area, 
for the element of area 2tt rdr is clearly 


S = 


dr 

2tt r 2 dr 


Eliminating S and </> from the foregoing expressions, there 
results 


dT 


2irf)n 


r s dr 



Integrating over the entire cylinder, the shear modulus 
for the entire solid cylinder of radius R and subject to 
the total torque T becomes 

2 IT 

U “ 7T0fl 4 * 

When l and R are expressed in cm., T in gram-cm., and 
d in radians, then the shear modulus is expressed in grams 
per sq. cm. 

In the apparatus used in this experiment, the angle V 
is determined by attaching mirrors to the rod under test 
and observing the deviations of these mirrors by telescopes 
and scales. If the scale reading change by a cm. with the 




36 PHYSICAL LABORATORY EXPERIMENTS 


application of torque, and d cm. be the distance between 
the mirror and scale, then the angular displacement of 
the rod and mirror is 

0 = i-tan -1 % = — radians 
2 d 2d 

when the deflection is small. 

Apparatus. Shear-modulus apparatus, micrometer 
caliper, meter-stick, and rods of steel and brass of various 
diameters. 

The apparatus for determining the shear modulus is 
shown in Fig. 15. One end of the rod to be tested is 
firmly clamped at the left support, and after affixing the 
lever arm in a horizontal position at the other end, the 
rod is centered by the large screw at the right support. 
For small samples, bushings are used which fit the rod 
and supports snugly, and are inserted in the supports so 
that the set pins engage the corresponding holes in these 
bushings. The two mirror clamps are fastened to the 
rod by pointed screws against Y-shaped edges, the dis¬ 
tance l between the clamps being the same as the dis¬ 
tance between the slots of the jig used while setting the 
mirror clamps in place. The scales and telescopes are 
supported at the top of the apparatus and are placed 
vertically over the mirrors. To take observations on a 
metal rod, place the scale pan on the spring hook of the 
lever arm, and then adjust the inclination of the mirrors 
and focus the telescopes so as to yield clear images of 
convenient scale divisions on the cross-hairs of the 
telescopes. Upon placing weights on the scale pan 
both mirrors will rotate, one more than the other, the 
difference of their scale deflections being the twist a. 

Procedure. Measure the diameter of the rod with 
the micrometer caliper at four different points along its 
length. Measure with the meter-stick the length of the 
lever arm, the distance between mirror clamps, and the 
distance from each mirror to its scale. After adjusting 


PHYSICAL LABORATORY EXPERIMENTS 37 


the mirrors, scales and telescopes into their proper 
positions, take a zero reading through the telescope. 
Then with 5, 10, 15, 20 and 25 pounds on the scale pan 
note the telescope readings. Make measurements on 



Fig 15. 

two rods either of different materials and of the same 
diameter, or of the same material but of different 
diameters. 

Observations and Conclusions. Record observa¬ 
tions and results for each rod as follows: 


















38 PHYSICAL LABORATORY EXPERIMENTS 


Material- 

Diam. of Rod 

(in.) Length of lever arm-cm. 

- Distance from mirrors to scale, d -cm. 

- Distance between mirror clamps, l -cm. 

- Average radius of rod, R -cm. 


Load 

in 

pounds 

Torque 

in 

gram- 

cm. 

T 

Scala Readings (cm.) 

Angu¬ 
lar dis¬ 
place¬ 
ment 
in 

radians 

e 

Shear 

Modulus 

in 

grams 
per sq. 
cm. 

n 

Left mirror 

Right mirror 

Twist 

a 

Read¬ 

ing 

Deflec¬ 

tion 

Read¬ 

ing 

Deflec¬ 

tion 

0 

5 

10 

15 

20 

25 


















































Compute the average shear modulus for each rod from 
the equation 

2 12T 

n tRW 

where 2T and 20 are the sums of the values in the col¬ 
umns headed T and 0 respectively. Express the result 
also in pounds per square inch. Compare results with the 
values given in Table IV. 

EXPERIMENT 10 
Specific Viscosities of Liquids 

Object. To determine the specific viscosities of water 
at several temperatures by Coulomb's method. 

Theory. Viscosity of a liquid is the resistance which 
it offers to changes of shape and is due to molecular 
friction between adjacent layers in the liquid which are 































































PHYSICAL LABORATORY EXPERIMENTS 39 


moving with different velocities. If a metal disk, which 
is wetted but not chemically acted upon by the liquid 
under test, is suspended by means of a long thin wire and 
set into rotatory vibration while immersed in that liquid, 
the various layers of liquid above and below the disk 
will be set in motion to different extents, and the disk 
will have its amplitude of vibration continually reduced. 
The liquid, due to its viscosity, exerts a retarding force 
on the disk which is proportional to the velocity of the 
vibrating disk. 

The motional equation of a body describing harmonic 
motion in a straight line and subject to a retarding force 
that is proportional to its velocity is 


S + 2 4* + r s = °’i 


where s is the displacement of the body from its position 
of equilibrium at the time t reckoned from that position, 
2k is a constant depending upon the retarding force, a 
is the maximum acceleration of the body, and r is its 
amplitude of vibration. The solution of this equation, 
found by placing s = e mt , is 

S = Ae mit + Be m *, 

where A and B are constants as yet undetermined, e is 
the base of the natural system of logarithms, and for 
oscillatory motion 

mi = — k + ja and m 2 = — k — ja , 


in which a = yj® - k 2 and j = V-l. Introducing 

these values of mi and m 2 and converting the imaginary 
exponential terms into their equivalent trigonometric 
forms by means of c ±j9 = cos 6±j sin 6, there results 


$ = e~ kt [(A + B) cos at + j(A — B) sin at J. 



40 PHYSICAL LABORATORY EXPERIMENTS 


Reckoning time and displacement from the position of 
equilibrium, it follows that s = 0 when t = 0; whence 
A + B = 0. Therefore 


s = (A — B)je kt sin at. 


By considering the time intervals elapsing between suc¬ 
cessive occasions when the velocity of the body is zero, 

it is seen that a = where T is the time of one complete 

T 

vibration. If C be the amplitude when t = —, then at 
any time t the displacement is 



When t = t = j T , t = etc., the amplitudes of 
vibration will be respectively 

si = C, 

52 = Ce~ kT 

53 = Ce~ 2kT . etc. 

Therefore the ratio of a linear displacement to the next 
preceding one in the same direction has the constant 
value of 


S3 _ $2 _ _ if 

S2 Si 

This result also applies to a body executing damped 
rotatory harmonic motion. Thus, if 8 represent the mean 
ratio of an arc of oscillation of a disk immersed in a 
viscous liquid to its next preceding arc of oscillation in 
the same direction, then the ratio of damping is 


PHYSICAL LABORATORY EXPERIMENTS 41 


where ft is a constant proportional to the retarding force, 
which in turn depends upon the viscosity of the liquid. 
The value of this constant, which may be termed the 
relative viscosity of the liquid, is obtained from the 
foregoing equation as 


k 


2.3026 

T 


logioS. 


Consequently the logarithm of the 
ratio of damping of a disk oscillat¬ 
ing in liquids serves as a measure 
of their viscosity. 




Apparatus. Viscosimeter, and stop-watch or elec¬ 
trical clock, shown above. 

The viscosimeter consists of a brass disk suspended by a 
thin vertical wire in a liquid contained in a dish and which 
can be warmed by an electric heater. The disk is pro¬ 
vided with a pointer which plays over a stationary grad¬ 
uated circle, thus enabling the measurement of the vibra¬ 
tion amplitude of the disk. 

Procedure. Place ice water in the viscosimeter 
dish and measure the temperature of the water. Dis¬ 
place the disk 180 degrees from its position of equilibrium 















42 PHYSICAL LABORATORY EXPERIMENTS 


and release it, exercising care to have the disk oscillate 
around its own center. Observe the indications of the 
pointer at the ends of nine successive complete oscil¬ 
lations. Again measure the temperature of the water. 
Displace the pointer and note the time of ten complete 
vibrations. Repeat these operations for water at about 
10 °, 20° and 40° C. Between tests heat the water slowly 
and avoid the formation of bubbles on the disk. 

The relative viscosities of other liquids at various tem¬ 
peratures may be determined in the same manner. 

Observations. Record observations of experiment 
for each of the four tests as indicated below; 


Viscosimeter Readings 


No. of 
Oscillation 


Test 1 


Degrees Ratio of 

Amplitude Damping 

of Disk 8 



Average ratio of damping, 5 = - 

{ at start - 

at end - 

mean - 

Time of 10 complete vibrations of disk-se ?. 

Time of 1 complete vibration of disk, T = - sec. 

Conclusions. Compute the relative viscosities of 
water at the four temperatures and plot the results in the 
form of a curve. Compare these values with the specific 
viscosities of water given in Table V. 



















PHYSICAL LABORATORY EXPERIMENTS 43 


EXPERIMENT 11 
Conformity of Air with Boyle’s Law 

Object. To determine how closely air at room 
temperature agrees with Boyle’s law over the range from 
half to double atmospheric pressure. 

Theory. The volume v of a perfect gas at constant 
temperature varies inversely as the pressure p upon the 
gas, or symbolically, pv = constant. All gases deviate 
somewhat from this law, especially near their regions of 
liquefaction. 

Apparatus. Boyle’s law apparatus, aneroid barom¬ 
eter, and thermometer. 

The apparatus used to illustrate the relation between 
the volume and pressure of a gas consists of a U-tube 
formed by two straight glass tubes connected at the 
bottom by a flexible rubber hose. The two glass tubes 
are mounted vertically on the frame and may be raised 
and lowered along a graduated scale and clamped in any 
desired position. One glass tube is graduated to read 
volumes directly in cubic centimeters, and is also pro¬ 
vided with a stop-cock at its upper end. Mercury is 
placed in the L’-tube and the gas to be investigated is 
confined in the graduated tube above the mercury sur¬ 
face. The heights of the mercury on both sides of the 
tube can be measured by a slider carrying a vernier 
which moves along the central scale. The index of the 
slider is a horizontal scratch on a mirror which extends 
back of each glass tube. In taking a reading on either 
column, the slider is moved until the image in the mirror 
of the pupil of the observer’s eye, the scratch on the mirror, 
and the top of the mercury column are seen to lie in one 
straight fine. 

The aneroid barometer consists of an air-tight cylin¬ 
drical chamber, the cover of which moves slightly in or 
oat with changes of atmospheric pressure. This motion 
is enhanc d by a delicate svstem of levers and is trans- 


44 PHYSICAL LABORATORY EXPERIMENTS 


mitted to a pointer which moves over a properly cali¬ 
brated scale. 

Procedure. After the apparatus has been leveled, 
entrap 6 cu. cm. of air in the graduated tube at atmos¬ 
pheric pressure. The stop-cock should then be kept closed 
until all observations have been made. Take a read¬ 
ing of the height of mercury in each tube. Increase 
the pressure by raising the open tube or lowering the 
graduated tube in such increments that the volume of 
enclosed air will be successively 5.5, 5.0, 4.5, 4.0, 3.5 
and 3.0 cu. cm., taking readings of mercury elevations 
in both tubes in cm. at each volume. Then decrease 
the pressure and observe the height of the mercury 
columns for enclosed gas volumes successively of 6, 7, 
8 , 9, 10, 11 and 12 cu. cm. Take readings of the ther¬ 
mometer and barometer at frequent intervals during the 
experiment. 

Variations in temperature of the entrapped air affect 
the accuracy of the experiment greatly; in fact, a rise of 
1 ° C. at room temperature introduces a change of about 
one-third of 1 per cent in the value of pv. Therefore 
avoid touching the tube containing the air under test. 
After each change of volume wait a minute or two before 
taking the readings of pressure and volume— why? 

Observations and Conclusions. Record the ob¬ 
servations of mercury elevations in the open and closed 
tubes for the various air volumes in tabular form. In 
another column record the absolute pressures ( p ) in cm. 
Hg. of the confined gas, obtained by adding to or sub¬ 
tracting from atmospheric pressure, expressed in cm. Hg., 
the differences in elevation of the two mercury columns. 
In the last column insert the computed products of vol¬ 
ume and absolute pressure for the different volumes 
of air. Plot two curves: one of pressure p in cm. Hg. 
against volume v in cu. cm., and the other of pv products 
against pressures p in cm. Hg. Determine the per¬ 
centage maximum deviation of the product pv from the 
value of this product at atmospheric pressure. 


PHYSICAL LABORATORY EXPERIMENTS 45 


EXPERIMENT 12 

Specific Gravity of Gases with Effusiometer 

Object. To determine the specific gravity of illumi¬ 
nating gas by means of the effusiometer and to determine 
the rate of gas consumption of several types of gas burners. 

Theory. The operating principle of an effusiometer 
is that light gases effuse more rapidly through a small 
orifice than do denser gases. Suppose a gas, of density 
8 grams per cu. cm., enclosed in a chamber under a 
pressure p dynes per sq. cm. above that of the surround¬ 
ing region, be allowed to escape through a small orifice 
of area a sq. cm. By equating the gain of kinetic energy 
of the gas per second to the loss of its potential energy 
per second, the speed of efflux in cm. per sec. is found to be 



Therefore two gases of densities 5i and 52 would effuse 
with velocities of v\ and V 2 respectively, such that 

Si = vl_ 

82 

Since the velocities of efflux are inversely proportional 
to the respective times ti and 1 2 required for the effusion 
of the same volume of the two gases through the same 
orifice, it follows that 

81 = tj? 

82 to 2 

Apparatus. Effusiometer, stop-watch or electrical 
clock, gas-meter, pressure gage, Bunsen, Meker and fish¬ 
tail burners. 

The effusiometer, Fig. 16, consists of a U-shaped glass 
tube, with a detachable metal fitting containing the effu- 


46 PHYSICAL LABORATORY EXPERIMENTS 



Fig. 16 


sion orifice with cover at 
the upper end of the 
graduated tube, and with 
a suction fitting at the 
other or suction tube. 
Water is placed in the 
lower part of the tubes. 
To take an observation 
with the instrument, the 
orifice fitting is removed, 
connection is made with 
the gas supply, the stop¬ 
cock at the top of the 
graduated tube is opened, 
and suction is applied 
until the water in the 
graduated tube falls be¬ 
low the first division. 
When the gas is thus 
drawn into the tube, 
close the stop-cock and 
replace the orifice fitting 
with its cover removed. 
Then open the stop-cock 
and observe the time 
necessary for the water 
to rise through several 
divisions of the grad¬ 
uated tube. 

Procedure. Draw air 
into the graduated tube 
and then allow it to 
escape, without using the 
effusion orifice. Repeat 
this process several times, 
and then leave the grad¬ 
uated tube full of air at 
the last operation. With 







PHYSICAL LABORATORY EXPERIMENTS 47 


orifice in place, note with a stop-watch the time h that is 
required for three divisions of the air volume to be dis¬ 
placed by the rising water. Take six such readings on 
air. Repeat the foregoing operations for illuminating 
gas to determine the time to for the same volume of gas 
to effuse through the same outlet. As the excess pres¬ 
sure p in this type of effusiometer becomes less as the 
water rises, the same three tube divisions must be used 
for all tests. 

As an addenda to this experiment, determine by means 
of a gas meter and watch the times for 1 cubic foot of 
illuminating gas to be burned at a Bunsen burner, a 
Meker burner and a fish-tail burner, for the purpose of 
obtaining an idea of the relative gas consumption of these 
burners. Measure the pressure of the gas at the burner. 

Observations. Make a tabular record of observations 
as below: 

Effusiometer Readings (sec.) 

Time for air to Time for illuminating 

effuse gas to effuse 


Aver. = h 

Aver. 

= <2 

Gas Consumed by Gas Burners 
Burner. Time to burn 1 cu. Gas pressure 

Rate of gas con¬ 

ft. of illuminating 

at burner 

sumption (cu. 

gas (sec.) 

(in. of water) 

ft. per hr.) 

Bunsen 

— 


Meker 

-— . 


Fish-tail 

— 



Conclusions. Compute the specific gravity of illu¬ 
minating gas with respect to air as unity. Taking 


















48 PHYSICAL LABORATORY EXPERIMENTS 


the density of air at 0° C. and standard pressure as 
0.001293 gram per cu. cm., calculate the density of 
illuminating gas under room conditions. 


EXPERIMENT 13 
Calibration Curve of Venturi Meter 

Object. To determine the quantities of water dis¬ 
charged through a Venturi meter under different heads, 
and to compare these values graphically with the 
theoretical discharges of incompressible, frictionless 
liquids. 

Theory. The Venturi meter depends for its operation 
upon the fact that the pressure in a constricted portion 
or throat of a tube through which a liquid flows is less 
than the pressure in the unconstricted portion. The 
total energy (kinetic and potential) of unit volume of 
liquid of density <5 flowing through the tube at velocity 
v under pressure p (or head h) is 

W = ^ 8v 2 + p = \8v 2 + Sgh, 

which is the same for a frictionless liquid at all points of 
the tube. If the velocity of the liquid be v and the head 
be h where the cross-sectional area of the tube is a, and 
the velocity be v\ and the head be hi where the con¬ 
stricted area is a\, then 

v 2 + 2 gh = vt 2 + 2ghi. 

Also, in an incompressible liquid, the rates of discharge 
of the liquid are the same a; all cross-sections, whence 


av = a\V\. 


Eliminating vi from the last two equations and solving 


PHYSICAL LABORATORY EXPERIMENTS 49 


for the discharge Q = av, there results as the theoretical 
discharge 

Q = Ml J- ~ = K Vh^h~i, 

Y a 1 — as 


where the discharge constant K = aai \ ——-—-. If 

>cr — as 

a and a\ are expressed in sq. cm., h and hi in cm., and 
(j in cm. per sec. per sec., then Q will be expressed in cu. 
cm. per sec. 

Apparatus. Venturi meter connected with water 
supply, vessel for collecting water, graduate, and watch. 

The Venturi meter consists of a horizontal tube with 
a constricted portion or throat and two vertical pressure 
tubes, one of which connects with the tube and the other 
with the throat. When water is passed through the 
meter, some water flows into the pressure tubes, and the 
heights to which it rises in the two tubes indicate the 
pressure heads of the water in the horizontal tube and in 
the throat. The theoretical discharge of water through 
the meter is a function of the difference of height of 
water in the pressure tubes. 

Procedure. Turn on the water through the meter, 
and before taking observations, see that all bubbles 
have been removed from the unconstricted portion of 
the meter having the pressure tube. When fairly con¬ 
stant conditions have been secured, direct the outflowing 
water into the collecting vessel for a few minutes. Ob¬ 
serve the heights of the water in pressure tubes during 
the discharge, note the time of discharge, and measure 
with the graduate the total amount of water col¬ 
lected during the test. Repeat the foregoing operations 
with different pressures, that is, with different values of 
h — hi. 

Observations. Record observations as indicated on 
th: next page: 







50 PHYSICAL LABORATORY EXPERIMENTS 


Constants of Venturi Meter 


Cross-sectional area of tube.(a) = -sq. cm. 

Cross-sectional area of throat.(ai) =-sq. cm. 

Discharge constant.( K ) =- 


Water Discharge of Meter 


Water in pressure tubes 
(cm.) 


Height Height 
at tube at thro i 
h h v 


Differ¬ 
ence 
h - 


Theoret¬ 
ical dis¬ 
charge 
(cu. cm. 
per sec.) 

Q 


Volume 
of water 
dis¬ 
charged 
during 
test 

(cu. cm.) 


Actual 


Time 
of dis¬ 
charge 
(sec.) 


dis¬ 
charge 
(cu. cm. 
per sec.) 

Q' 



Conclusions. Calculate from the equation the theo¬ 
retical discharge Q and from the. tests the actual dis¬ 
charge Q' of water during each test, and insert these 
values in above table. Plot a curve with Q as abscissas 
and Q' as ordinates. 

EXPERIMENT 14 

Velocity of Sound—Specific Heats of a Gas 

Object. To measure the velocity of sound in a metal 
rod and in air, to determine the pressure of the atmosphere 
and its density, and to calculate the ratio of the specific 
heat of air at constant pressure to that at constant volume. 

Theory. To ascertain the velocity of sound in a gas, 



































































PHYSICAL LABORATORY EXPERIMENTS 51 


consider a wind of such velocity as to oppose exactly 
the advance of sound waves, traveling with the same 
velocity in the gas. Each portioji of the gas assumes 
in turn the states of condensation and rarefaction im¬ 
posed by the sound waves, but these states are stationary 
in space due to the opposing wind. The pressure, 
volume per unit mass, and the velocity of the gas par¬ 
ticles (medium being considered at rest) vary from point 
to point along the direction of propagation. Let these 
characteristics be respectively p, w and v at one point 
and be p', w' and v' at another, point fixed in space. 
Assuming the sound waves to retain their wave-shape 
as they advance, there will be no accumulation nor dimi¬ 
nution of gas between the two reference points, and 
therefore the masses of gas which pass these points per 
unit time and per unit area must be equal, or 


v _ v 
w w' 


These masses have different velocities and therefore 
different momenta. The gain or loss of momentum 
of a prism of gas in unit time, due to the difference of 
pressure at the two reference points, is therefore 


p-p 


v , 

=—/ 

w 


V 

— V. 

w 


Eliminating v' from the foregoing equations, and solving 
for v, there results as the velocity of the sound relative 
to the gas ’ _ 

. • . ( 1 ) 


P — P' 2 l E 

v = \ — — W 2 = A/T"’ * 

Y w —W Yd 


where E= V , — is the bulk modulus of elasticity of the 
w —to 


gas, and 5 = — is its density. 
w 







52 PHYSICAL LABORATORY EXPERIMENTS 

As the compressions and rarefactions of the medium 
when traversed by sound waves occur with great rapidity, 
the heat developed by compression is not diffused, nor 
is heat absorbed from the surroundings during rarefac¬ 
tions. In consequence, the modulus of elasticity E in 
the foregoing expression is the volume coefficient for 
adiabatic conditions. This coefficient may be expressed 
in terms of the isothermal modulus of elasticity e and 
the specific heats of a gas under constant pressure and 
constant volume, respectively c p and c v , namely 

E = e C Jt = e y t .(2) 

C D 


where 7 is the ratio of the two specific heats of the gas. 
(Refer to § 184 of Reed and Guthe “ College Physics.”) 
The modulus of elasticity under isothermal conditions 
can be ascertained by considering a volume V of gas at 
pressure p to have its volume reduced by dV under an 
increment of pressure dp. Then by Boyle’s law 


p V =(p+dp)(V-dV), 


which, by neglecting the small product dp-dV, reduces to 



Combining equations (1), ( 2 ) and (3), there is obtained 
Laplace’s formula for the velocity of sound in a gas, 
namely, 



When p is the pressure of the gas in dynes per sq. cm. 
and d is its density in grams per cu. cm., then v is the 





PHYSICAL LABORATORY EXPERIMENTS 53 


velocity of sound in cm. per second. In order to de¬ 
termine 7 experimentally from this equation, the factors 
v, p and 8 must be measured, the methods of their measure¬ 
ment being next considered. 

A metal rod of length L cm. clamped at its center is 
set into longitudinal vibration in its fundamental mode 
and its frequency of vibration is found to be /. Then 
the velocity of sound in the rod in cm. per second is 

v. = 2/L, . ..(5) 

since the length of the rod is one-half of a wave-length. If 
one end of the rod project into a closed tube of proper 
length and that end be provided with a light disk which 
fits loosely into the tube, then the rod, when placed in 
vibration, will set up stationary waves in the gas enclosed 
in the tube. Cork filings strewn inside the tube will 
collect at points where the gas particles have their great¬ 
est amplitudes. The average distance l cm. between 
centers of successive groups of the filings will be half of 
a wave-length of the sound in the gas; whence the velocity 
of sound therein is 

v = 2fl = v r y .(6), 

L 

cm. per second at the temperature at which the experi¬ 
ment is performed. 

The pressure of a gas at any temperature may be de¬ 
termined by measuring the height h cm. of a column of 
mercury that it can support. Thus the pressure in dynes 
per sq. cm. is 

p = hdg, .(7) 

where d is the density of the mercury in grams per cu. 
cm. and (j is the acceleration of gravity in cm. per sec . 2 
If air at atmospheric pressure be under investigation 




54 PHYSICAL LABORATORY EXPERIMENTS 


the value of h can be read from a mercurial or an aneroid 
barometer. 

When several gases are mixed, the total pressure of 
the mixture is equal to the sum of the pressures exerted 
by the component gases individually. Thus, atmospheric 
pressure is made up of the pressure of dry air and that of 
the water vapor present. If these component pressures 
be respectively p a and p w , then atmospheric pressure is 


p' = Va+Vw cm. of Hg. 

The value of p w may be determined from measurements 
of the dew-point (see Experiment 21) in connection with 
Table XII. The densities 5o of most gases are known at 
76 cm. of Hg.(po) and 0° C. from carefully performed 
experiments; the values for a few gases are given in 
Table VI. The density of a dry gas at any other pressure 
p a and temperature t is 

s _ s P °. 273 

0q — 0 0 * • 

po 273+* 

Taking the density of dry air at 76 cm. of Hg. and 0° C. 
as 0.001293, and the density of water vapor relative to 

air at the same temperature as — = 0.62, the density of 

5a 

the atmosphere at temperature t °C and pressure p cm. of 
Hg. is 

a—o.ooi2»(g+^”)JL 

= 0.004645.... (8) 
273-H 

where the pressure of water vapor p w is also expressed 
in cm. of Hg. 

Having determined the value of v from equation (6), 
p from equation (7) and d from equation (8), these values 






PHYSICAL LABORATORY EXPERIMENTS 55 


are substituted in equation (4), which can be rewritten 
in the form 



in order to find the ratio 7 of the specific heat at con¬ 
stant pressure to that at constant volume. 

Apparatus. —Kundt’s tube with metal rod, toothed 
wheel driven by a motor rotator, motor rheostat, tach¬ 
ometer or speed indicator, aneroid barometer, hygrometer 
and thermometer. 

The Kundt’s tube is a glass cylindrical tube provided 
with metal fittings at its ends and mounted in a hori- 


Fig. 17. 



zontal position as shown in Fig. 17. A metal rod is 
inserted into the tube and clamped at its middle point 
at the left-hand fitting. At the other end of the tube a 
tight-fitting stopper can be moved in or out and be 
clamped in any desired position. In this way the length 
of the gas column between the end of the rod and the 
stopper can be properly adjusted. Measurements on 
many gases at various temperatures may be made with 
this device. 

Procedure and Observations. —Clamp the metal 
rod at its center and set it into longitudinal vibration by 
rubbing one end of the rod in the direction of its length 
with resined chamois, endeavoring to obtain a clear and 
loud tone. Start the motor rotator carrying the toothed 
wheels and allow a spring to press against the revolving 
teeth of one of the wheels. Adjust the speed of the 
motor by manipulating the rheostat until the sound 








56 PHYSICAL LABORATORY EXPERIMENTS 


emitted by the vibrating spring is exactly of the same 
pitch as that produced by the rod, and then measure this 
speed by means of a tachometer or a speed indicator. 
Knowing the number of teeth on the wheel employed in 
this measurement and the speed of the wheel in revolu¬ 
tions per second, the frequency of vibration / of the rod 
is obtained as their product. Then measure the length 
of the rod in cm. and calculate the velocity of sound in 
the material of which the rod is composed. Compare the 
result with the values given in Table XVI. 

Place a disk upon one end of the rod and insert that 
end into the Kundt’s tube and fasten the rod at its center 
to the clamping bushing. Distribute cork filings evenly 
over the bottom of the tube and then set the rod in 
vibration. If the filings do not show a disturbance, 
move the stopper in small steps in either direction until 
a position is found which will cause the filings to assume 
well-defined ridges along the tube corresponding to the 
position of antinodes of the waves in the air. Measure 
the average distance between centers of successive ridges 
and also observe the temperature of the room. 

Observe the atmospheric pressure by reading the 
aneroid barometer in inches of Hg. and reduce this value 
to dynes per sq. cm. Determine the dew-point by means 
of a Daniell hygrometer or a hygrodeik, as indicated in 
Experiment 21, and ascertain the pressure of water vapor 
in the atmosphere. 

Conclusions. —From the tabulated observations de¬ 
termine the velocity of sound in air at atmospheric pres¬ 
sure and room temperature. Compute from the baromet¬ 
ric and hygrometric observations the density of the 
atmosphere in grams per cu. cm. Finally calculate the 
ratio of the specific heats of air from Laplace’s formula 
and compare the result with the value given in Table VII. 


PHYSICAL LABORATORY EXPERIMENTS 57 


EXPERIMENT 15 


Coefficient of Expansion of Gases by Air Thermometer 

Object. To determine the coefficient of expansion of 
air by means of a constant volume air thermometer. 

Theory. Consider a gas at 0° C. to occupy a volume 
v 0 under a pressure p n , while at t° C. it occupies a volume 
v t under a pressure p,. Then according to the Boyle 
Gay-Lussac law for perfect gases 

VtVt = PoVoil + at), 

where a is the coefficient of expansion of the gas« If the 
volume remains unchanged while the temperature is 
varied by a known amount, measurements of the pres¬ 
sures enable the determination of the expansion coeffi¬ 
cient, since 

a = a r p» . 

Pot . v 

Fig. 18 shows the general design of the air thermometer 
employed. The gas under inves¬ 
tigation is enclosed in the bulb A, 
which is connected with a U-tube 
containing mercury. The volume 
of the enclosed gas may be kept 
constant during a test by raising 
or lowering tube B so that the 
surface of the mercury in tube C 
just touches the index point I. 

Let the height of this index above 
some convenient datum be h and 
the heights of the mercury in tube 
B when the bulb is surrounded 
by melting ice and then by steam 
be respectively h 0 and h t , as indi¬ 
cated in the figure. Since the 

pressure on the gas is proportional to the difference 



Fig. 18. 
















58 PHYSICAL LABORATORY EXPERIMENTS 


of the heights of the two mercury columns, it follows 
that 

h t — h 0 

a ~ t(H + h 0 - h)’ 

where t is the temperature of steam, and H is the baro¬ 
metric height. The temperature of steam in degrees C. 
may be computed from the barometric height H cm. Hg. 
by using the formula 

t = 100 + 0.375 (H - 76). 

The foregoing simple expressions for a are not directly 
applicable to the present experiment because the volume 
of the bulb increases when heated from 0 ° to t° C., and 
also because a small portion of the gas under test, namely 
that in tube C, does not change its temperature greatly 
from room temperature. Therefore correct expressions 
for the volumes v 0 and v of the gas at the respective 
temperatures must be obtained. Also, the pressures 
should be corrected for the expansion of the mercury 
in the columns if the temperature of these columns be 
higher during the observations with steam than during 
those with ice surrounding the bulb. 

Let t\ and k be the respective temperatures in degrees 
C. of the mercury columns at the time when the ice and 
steam readings are taken, as indicated by a thermometer 
placed along the columns. Then the pressures reduced 
to 0 ° C. at the temperatures of 0° and t° C. are 

P° = H + t + o.oooisti = H + - W 1 ~ 0.00018 <,), 

approximately, and similarly 

p t = H + (h t - h)( 1 - 0.00018^), 

where the constant 0.00018 is the coefficient of expansion 
of mercury. 




PHYSICAL LABORATORY EXPERIMENTS 59 


Let the volumes of the bulb A and the tube C at 0° C. 
be V and v respectively. Then the volume that the gas 
would occupy at pressure p 0 were its temperature 0° C. 
throughout is 


V n = 


V + 


v 

l + 


and the volume which the gas would occupy at pressure 
Vt were its temperature t° C. throughout is evidently 

!'« = F(1 + 0.000025 t) + t a< , 

1 + at2 

where 0.000025 is the coefficient of expansion of glass. 
Substitute the foregoing values of v 0 and v t in the first 
equation and divide through by V, there results 

B [l+0.000025,+ 

= + F (1 + a ,,)) (1 + ot) • 

Rather than seek a general solution for a, this equation 
may be put in the more convenient form 

, P«(! + F( 1 +a £j) - P. 


in which a appears also in the right-hand member, but 
only in the small correction factors involving Hav¬ 


ing ascertained the values of p 0 , p h t, ti and by experi¬ 
ment, choose some reasonable value for a and insert it 
in the factors (1 + a£i) and (1 + afo) and then solve for 
a by the last equation. Thereafter introduce this com- 













60 PHYSICAL LABORATORY EXPERIMENTS 



Fig. 19. 














PHYSICAL LABORATORY EXPERIMENTS 61 


puted value in the correction factors and again solve the 
foregoing equation, this time obtaining the final value 
for the coefficient of expansion of the gas. 

Apparatus. Air thermometer, .aneroid barometer, 
mercury thermometer, ice and steam baths, Bunsen 
burner, and tripod. 

The air thermometer to be used is shown in Fig. 19. 
It consists of a thin cylindrical glass bulb which is joined 
to the chamber having the index wire by means of a 
glass tube of small bore. This chamber communicates 
through a stop-cock and a flexible hose with a straight 
open glass tube, both glass parts being attached to metal 
fittings which can be clamped to the vertical guide 
rods at any desired heights. The height of the bulb 
should remain the same throughout this experiment. An 
amount of mercury is placed in the tube which is sufficient 
to bring the mercury surfaces in the two columns to suit¬ 
able heights. The heights of the mercury surfaces in 
any test are obtained by means of a slider which moves 
along a vertical scale graduated into mm., the slider 
carrying a vernier and a mirror with a horizontal scratch. 
When the slider is properly set to indicate the height of 
a mercury column, the image in the mirror of the observer’s 
eye, the scratch on the mirror, and the top of the mercury 
column should be seen in one line. In this air ther¬ 
mometer the ratio v/V =0.024. 

Procedure. Observe the height h of the wire index. 
After the bulb has been filled with dry air, place the vessel 
of the ice bath around the bulb of the air thermometer 
and carefully drop small pieces of cracked ice into the 
vessel until the bulb is completely surrounded by ice. 
After the air ceases to contract, a process requiring about 
ten minutes, adjust the level of the open column so that 
the mercury in the other column will just touch the wire 
index; then observe the height of the mercury h 0 in 
the open column. Repeat this observation by making 
another independent setting of the slider. Record the 
reading t\ of a mercury thermometer supported between 


62 PHYSICAL LABORATORY EXPERIMENTS 


the two columns and with its bulb near the wire index. 
Take also a reading of the aneroid barometer. 

Remove the ice bath carefully and replace it by the 
steam bath. Light the gas under it and then put the 
cover in place. As steam forms around the bulb raise 
the open tube so as to maintain the mercury surface in 
the other tube near the reference point. When the air 
ceases to expand, that is, when the gas in the bulb has 
reached the temperature of steam, t° C., adjust the 
mercury exactly on the wire index and note the height h t 
of the mercury in the open column. Readjust and take 
another observation. Record the temperature to now 
indicated by the mercury thermometer. Then remove 
the vessel and lower the open column so that the mer¬ 
cury cannot enter the bulb when the gas contracts in 
assuming room temperature. 

Observations and Conclusions. Reduce the barom¬ 
eter reading to cm. Hg. and compute the gas pressures 
at 0° and t° C. Calculate the temperature of steam t 
under existing conditions and finally determine the coeffi¬ 
cient of expansion of air. Compare this result with the 
theoretical value given in Table VI. 


EXPERIMENT 16 
Specific Heats of Solids 

Object. To determine the specific heat of copper by 
the method of mixtures. 

Theory. A mass of m grams of copper is heated to 
a temperature h° C. and then dropped into M grams 
of water at C. contained in a calorimeter whose 
water equivalent is k. If the resulting temperature be 
t ° C., then the specific heat of copper will be 

8 = (AT + *?)(<- fe) 
m(ti — t) ’ 



PHYSICAL LABORATORY EXPERIMENTS 63 


if radiation be ignored or be compensated for as indicated 
later on. 

In the experiment it will be found impracticable to 
have the thermometer, which is used in measuring the 
temperature of the heated copper, entirely exposed to 
the same temperature as the bulb. Consequently the 
thermometer will read too low, and a correction for 
stem exposure should be made. If the reading of the 
thermometer be t' ° C., the temperature of the exposed 
stem as determined by another thermometer be t 3 ° C., 
and the length of the exposed mercury thread in degrees 
be n, then the corrected reading of the thermometer (or 
the true temperature of the copper) will be 

ti = t' + 0.000156n(C - Q + c, 

where the numerical constant is the coefficient of apparent 
expansion of mercury in glass per degree C., and the 
constant c is the calibration 
correction arising from irreg¬ 
ularities in the diameter of 
the thermometer bore. 

Apparatus. Calorimeter 
and steam jacket mounted 
on convenient stand, boiler, 
balance with weights, Bunsen 
burner, bundle of copper 
scraps, three mercury ther¬ 
mometers, and tripod. 

The calorimeter, steam 
jacket and protecting shutter 
are shown in Fig. 20. The 
device illustrated includes a 
polished calorimeter which 
is supported by strings within 

another polished metal vessel that in turn is placed in a 
wooden box. This box carries a support for holding the 
thermometer used to record the temperature of the calo- 



Fig. 20. 















64 PHYSICAL LABORATORY EXPERIMENTS 


rimeter contents. The heater consists of a steam jacket 
which surrounds a cylindrical chamber that is open at its 
lower end but is closed at the top by a removable cover. 
The copper scraps to be measured for specific heat are 
suspended in the heating chamber by means of a string 
attached to the cover. The temperature of the copper 
is determined by a thermometer which is inserted through 
the cover to the proper depth so that its bulb will be 
alongside the copper scraps. To transfer the specimen 
from the heater to the calorimeter, the shutter is raised, 
the calorimeter is moved directly under the heating 
chamber, the string holding the copper is released and 
the copper is then quickly lowered into the calorimeter. 

The mass of the calorimeter used is 126.5 grams and 
its specific heat is 0.094. The approximate volume of 
the immersed part of the calorimeter thermometer is 
1 cu. cm., and the product of specific heat and density 
both for mercury and for glass is nearly 0.46. There¬ 
fore the water equivalent of the calorimeter and ther¬ 
mometer is 

k = 126.5 X 0.094 + 0.46 = 12.35 grams. 

Procedure. Weigh the bundle of copper scraps and 
then suspend it in the heating chamber. After partially 
filling the boiler with water, ignite the gas at the Bunsen 
burner beneath the boiler. Pass the issuing steam 
through the steam jacket and from there to a condensing 
vessel, meanwhile keeping the calorimeter protected 
from the heater by lowering the wooden shutter. When 
the temperature of the heater chamber has been constant 
for some minutes, pour about 250 grams of water into 
the calorimeter, the water having a temperature approx¬ 
imately 3° C. below that of the room. .Observe the 
temperature indicated by the thermometer located in 
the heater chamber, then measure the temperature of 
its exposed stem, and thereafter note the reading of the 
thermometer in the calorimeter, estimating tenths of 


PHYSICAL LABORATORY EXPERIMENTS 65 


divisions in each case. Immediately raise the shutter, 
slide the calorimeter under the heater, lower the bundle 
of copper scraps into the calorimeter quickly but without 
splashing any water, withdraw the calorimeter, lower the 
shutter, slowly agitate the water by raising and lowering 
the copper by its suspending thread, and note accurately 
the final temperature of the water. It will be observed 
that the final temperature is roughly as much above room 
temperature as the latter was above the temperature of 
the calorimeter and contents just prior to the introduc¬ 
tion of the copper; thus the gain of heat by absorption 
will in a large measure neutralize the loss of heat by radia¬ 
tion. 

Observations and Conclusions. Record observa¬ 
tions in tabular form, correct the thermometer readings, 
and calculate the specific heat of copper. Compare this 
result with the value given in Table VIII. 

EXPERIMENT 17 


Heat Equivalent of Electrical Energy 


Object. To ascertain the mechanical equivalent of 
heat by the electrical method, or, in other words, to 
determine the heat equivalent of electrical energy. 

Theory. An electric heater is placed in a calorimeter 
containing water and the electrical energy expended as 
well as the heat developed is measured. The ratio of 
these quantities is the mechanical equivalent of heat. 
If the heater takes I amperes at an electromotive force 
of E volts for T seconds, the electrical energy expended is 
EIT joules. Let the mass of water in the calorimeter 
be M grams, the water equivalent of the heater and 
calorimeter be k grams, and the temperature rise be 
t ° C., then the mechanical equivalent will be 


J = 


EIT 

t(M + k) 


joules per calorie. 



66 PHYSICAL LABORATORY EXPERIMENTS 


The temperature rise t is obtained from the tempera¬ 
ture t\ of the calorimeter and contents at the instant when 
the current is turned on, the temperature thereof at 
the moment when the current is turned off, and the correc¬ 
tion factor which takes care of radiation. If n and r<i 
be the rates of rise of temperature in degrees per second 
of the calorimeter respectively immediately before the 
current is turned on and just after it is turned off (rates 
are considered negative if temperature falls), t r be the 
average room temperature, and t a be the average tem¬ 
perature of the calorimeter while the current flows 
through the heater, then the corrected temperature rise 
may be expressed as 


t — t2 — ti + 


(r 1 - r 2 )T(t a - t r ) 
t2 ~ h 


It will be observed that when t 2 = t r the temperature 
rise is simply — h, for then the radiation correction 
reduces to zero. 

Apparatus. Calorimeter, electric heater, series resist¬ 
ance, voltmeter, ammeter, two thermometers, balance 
with weights, and watch. 

The heater consists of a coil of wire within a metal 
tube and is designed to carry a current of about 2 amperes. 
It must be connected in series with a resistance when sup¬ 
plied with current from 110-volt supply circuits. The 
heater must be wholly immersed in water before current 
is allowed to flow through it, otherwise there is like¬ 
lihood of burning out its coil. The specific heat of the 
heater is 0.10, and of the calorimeter and stirrer is 0.09. 

Procedure. Weight the heater and the empty calo¬ 
rimeter separately. Nearly fill the calorimeter with a 
measured amount of water having a temperature of from 
5 to 10° C. Suspend the heater in the water in a vertical 
position, but have its top project about an inch above 
the water surface so that no water can reach the con¬ 
nection terminals. Take readings of calorimeter tempera¬ 
tures at exactly one-minute intervals for 35 minutes, 



PHYSICAL LABORATORY EXPERIMENTS 67 


stirring the water continuously with the stirrer. One- 
half minute after the eighth reading turn on the cur¬ 
rent through the heater and exactly 20 minutes later 
turn off the current. Voltmeter and ammeter readings 
should be taken at one-minute intervals midway between 
thermometer readings. Several observations of room 
temperature are to be made during the test. All ther¬ 
mometer readings must be made to tenths of a degree C. 

Observations. Before making the test, prepare a 
table of five columns having the following captions: 
time in hours and minutes, temperature of calorimeter, 
temperature of room, voltmeter reading, and ammeter 
reading. After taking and recording the observations, 
determine the average room temperature, and the average 
readings of the voltmeter and ammeter. Compute the 
mean temperature of the calorimeter, t a , during the time 
that current flows through the heater, by adding all 
temperatures of the calorimeter taken during that time 
and dividing by the number of readings. 

Conclusions. Calculate the water equivalent of the 
calorimeter and heater. Plot the observations of calo¬ 
rimeter temperatures against time as abscissas, draw 
straight lines through the points representing the con¬ 
ditions before current flows through the heater and those 
after it ceases to flow, and connect the other points 
by a suitable curve. Determine from this graph the 
temperatures ti and at the junctions of the three fines, 
and also the rates of heat exchange n and r 2 . Show room 
temperatures on the same curve sheet. Apply instru¬ 
ment corrections to the readings of the thermometers 
and of the electrical instruments. Compute the temper¬ 
ature rise of the calorimeter corrected for radiation and 
absorption, and then determine the heat equivalent of 
electrical energy. 


68 PHYSICAL LABORATORY EXPERIMENTS 


EXPERIMENT 18 
Mechanical Equivalent of Hea' 

Object. To determine the mechanical equivalent of 
heat in converting mechanical energy into heat by friction. 

Theory. In the apparatus employed in this experi¬ 
ment heat is developed by the friction between a rotating 
cylindrical drum of thin brass and a silk belt wound 
around the drum and held approximately stationary in 
position by means of adjustable weights fastened to the 
ends of the belt. The drum, or calorimeter, contains 
a measured amount of water and the heat developed 
by friction is determined by observing the temperature 
rise of the calorimeter and contents. Let the diameter 
of the drum at its rubbing surface be d cm., the net 
weight holding the belt in equilibrium be M grams, and 
the number of revolutions of the drum to produce a given 
temperature rise be n; then the mechanical work done 
in ergs is 

W = irdnMg, 

where the acceleration of gravity g is expressed in cm. per 
sec. per sec. If the calorimeter contains m grams of 
water and the water equivalent of the drum is k grams, 
and if the temperature rise be t° C., then the heat de¬ 
veloped in calories is 

H = (m + k)t; 

whence the mechanical equivalent of heat is 
r _ irdnMg 

J ~ "(m + k)tW Joules per calone ' 

Apparatus. Callendar’s mechanical-equivalent ap¬ 
paratus with thermometer, weights and electric motor, 
a 250-cu. cm. standard flask, thermometer, outlet nozzle, 
funnel and beaker. 



PHYSICAL LABORATORY EXPERIMENTS 69 


Callenclar’s apparatus, Fig. 21, consists of a calorimeter 
drum mounted on a horizontal axis for rotation either 
by hand or by an electric motor. A silk belt is wound 
around the drum to form one and a half turns, and a 
weight holder is attached to each end of the belt. A 
mass of 2 or 4 kilograms is placed on the rear weight holder 
and one or more small masses of 25 or 50 grams, are 



Fig. 21. 


placed on the front weight holder as required to main¬ 
tain floating equilibrium of belt and weights during the 
rotation of the drum. A spring balance fastened to the 
horizontal stage and to the front weight holder auto¬ 
matically maintains equilibrium by acting in opposition 
to the front weight. When the friction between the belt 
and drum increases the large rear weight is lifted and 
the front weight holder and weights descend, thereby 
placing a part of their weight upon the spring balance 






70 PHYSICAL LABORATORY EXPERIMENTS 


and thus lessening the belt tension and decreasing fric¬ 
tion. The weights of the front and rear weight holders 
are the same. Let p and P be the respective masses in 
grams of the weights placed on the front weight holder 
and of the large weights placed on the rear weight holder. 
Then, if q be the average spring balance reading, the net 
weight acting on the belt is 

M = P — p + q grams. 

A revolution counter is provided to register the number 
of turns of the calorimeter. The rise of temperature of 
the calorimeter and contained water is observed by means 
of a mercury thermometer, inserted through the central 
opening of the drum, whose bulb is bent around so that 
it will be fully immersed in the water. The water 
equivalent of the calorimeter and thermometer is 35.6 
grams, and the diameter of the drum is 15.0 cm. 

Procedure. Insert the outlet nozzle in the end of 
the drum near the rim and verify the fact that the drum 
contains no water. Put the silk belt in position, place 
2 or 4 kilograms on the rear weight holder, and place 
several small weights on the front holder, the number 
being adjusted by trial so that on turning the drum at 
a moderate speed the weights will be held in floating 
equilibrium between their stops. Measure out 250 cu. 
cm. of cold water in the standard flask, the temperature 
being about 6° C. below room temperature, and pour this 
water into the calorimeter drum. Carefully insert the 
bulb of the curved thermometer in the axial opening of the 
drum and fasten the thermometer in its support so that 
the bulb will be immersed in the water. Start the motor 
with 110 volts impressed upon its field circuit but with a 
lower voltage on the armature, this voltage being regulated 
by a rheostat in series with the armature. As soon as 
steady running is established, the experiment is begun 
by making simultaneous readings of the revolution counter 
and the calorimeter thermometer. Thereafter at fre- 


PHYSICAL LABORATORY EXPERIMENTS 71 


quent intervals read the spring balance and occasionally 
observe the temperature of the room. Should it be 
necessary during the course of the experiment to vary 
the weights on the front holder to maintain equilibrium, 
the temperature intervals during which the several weights 
act should be noted so that a weighted average for p may 
be computed. When the curved thermometer indicates 
a temperature of the water as much above the average 
room temperature as it was below this value when the 
first reading was taken, read the revolution counter. 
Then stop the motor, detach the thermometer, and 
remove the water from the calorimeter. 

Observations and Conclusions. Record the values 
of the rear weight P and the front weight p. Determine 
the average reading of the spring balance, q, the number 
of revolutions of the drum, n, and the temperature rise 
of the calorimeter and contents, t. Compute the amount 
of work done, the amount of heat developed, and lastly 
the mechanical equivalent of heat. 

EXPERIMENT 19 
Heat of Fusion of Ice 

Object. To determine the heat of fusion of ice with 
the Bunsen ice calorimeter. 

Theory. The Bunsen ice calorimeter consists of a 
peculiarly shaped glass vessel and tube as shown in Fig. 
22. The glass vessel consists of an inner receiving tube I 
open at the top and surrounded by a chamber C filled 
with distilled water. The lower part of this chamber is 
occupied by mercury, which extends up the vertical tube 
U and into the long horizontal calibrated tube T. The 
entire chamber and vertical tube are kept at 0° C. by 
being placed in crushed ice contained in an earthenware 
vessel V. By placing ether in the inner tube I and then 
evaporating it by forcing air from a blower through it, 
some of the water in C will freeze around the inner tube. 


72 PHYSICAL LABORATORY EXPERIMENTS 


Since the density of ice is less than that of water, the 
formation of ice will cause some mercury to flow out the 
end of tube T. When the end of the mercury column 
in this tube remains stationary the ice calorimeter is 
ready for use. 

If an electric heating coil be placed in the inner tube 
for t seconds some of the ice in C will melt and the end 
of the mercury thread will retreat say d divisions. Let 
one division of the tube represent a volume of k cu. cm., 
and let the current taken by the heating coil be I amperes 



under an electromotive force of E volts. Then the heat 
developed will be 

TT Elf . . 

H = 0 calories, 

4.2 

and the amount of ice melted will be 

dk 

m = 0.0907 

where 0.0907 is the difference of the volumes of unit 
masses of ice and water at 0° C. Therefore the heat 
of fusion of ice in calories per g' am is 


























PHYSICAL LABORATORY EXPERIMENTS 73 


Apparatus. Bunsen ice calorimeter, tube support, 
blower, ether, electric heating co.l, rheostat, ammeter, 
voltmeter, stop-watch, funnel and ice. 

The main features of the calorimeter have already 
been described. The junction of the vertical tube U and 
the horizontal tube T is effected 
by an intermediate glass tube G, 
as illustrated in Fig. 23. To set 
up the calorimeter parts, nearly 
fill the enlarged upper end of tube 
U with mercury, place tube G 
firmly in position, insert graduated 
tube T so that the through-hole a 
in the attached stop-cock is ver¬ 
tical, pour mercury in cup M, 
slightly loosen the stop-cock in 
order that tube G will fill with 
mercury, turn stop-cock so that 
a little mercury from cup M will Fig. 23. 

flow directly into tube T, and 

finally turn stop-cock 180 degrees to the position shown 
in the figure, thus completing the mercury column from 
the calorimeter chamber to the graduated tube. 

Procedure. Nearly fill the earthenware jar with 
cracked ice and then fill the interstices with ice-cold water. 
After about 15 minutes complete the mercury column to 
the graduated tube, and then evaporate ether in the inner 
receiving tube. The formation of the ice coating around 
this tube will be indicated by a rapid movement of the 
end of the mercury thread in the graduated tube. Con¬ 
tinue the evaporation of ether until about 0.2 cu. cm. 
of mercury has been forced out of tube T, or until the 
ether then remaining in the receiving tube has dis¬ 
appeared. After the mercury in the graduated tube 
becomes stationary, insert the platinum heating coil in 
the receiving tube, and close its electrical circuit, which 
includes a voltmeter and an ammeter. As the end 
of the retreating mercury column passes some convenient 









74 PHYSICAL LABORATORY EXPERIMENTS 


reference point, start the stop-watch. Note the indica¬ 
tions of the voltmeter and ammeter. When the mer¬ 
cury thread has shortened 200 or 300 millimeter divisions, 
stop the watch and note the elapsed time. Quickly take 
another set of observations as before, and then open the 
circuit of the heating coil. The volume per millimeter 
division of tube, k, will be given. 

Observat ons and Conclusions. Record the data 
for the two determinations in parallel columns and com¬ 
pute the average value of the heat of fusion of ice. Refer 
to Table X. 


EXPERIMENT 20 
Heats cf Combustion of Fuels 

Object. To determine the heat developed in burning 
illuminating gas with the Junker’s continuous-flow 
calorimeter. 

Theory. In this determination a measured volume 
of gas is burned at a Bunsen burner in an air chamber 
which is surrounded by a water jacket, and the heat is 
absorbed by the water which flows in a steady stream 
through this jacket. Let the mass of water which passes 
through the jacket while v liters of gas are burned be M 
grams, and let the temperatures of the water on entering 
and leaving be t' and t° C. respectively. Water vapor 
is formed by the combustion of gas and subsequently 
condenses and leaves the chamber as m grams of water 
at a temperature ti° C. Then the heat of combustion 
of the gas in calories per liter is 

h = M(t - Q - m(536 + [100 - L]) 
v ’ 

where the value 536 is the heat of vaporization of water 
in calories per gram. In the foregoing, the volume of 
gas v should be the volume as measured at 0° C. and 76 
cm. Hg. pressure. In the experiment the gas to be burned 




PHYSICAL LABORATORY EXPERIMENTS 75 


is first passed through a gas meter and a pressure regulator, 
the latter being equipped with an open water manometer. 
The pressure of the gas is atmospheric pressure H cm. Hg. 
augmented by the height of mercury which corresponds 
to the difference d cm. of the water levels in the two arms 
of the manometer. If the gas-meter readings indicate 



Fig. 24. 


that a volume of V liters of gas has been burned, and its 
temperature before combustion is t"° C., then the equiva¬ 
lent volume at 0° C. and 76 cm. Hg. pressure will be 


v = 



76(1 + 0.003672") 


liters, 


where the constant 13.6 is the specific gravity of mercury. 






















76 PHYSICAL LABORATORY EXPERIMENTS 


Apparatus. Junker’s calorimeter, gas meter, pressure 
regulator, two graduates, large vessel, aneroid barometer, 
five thermometers, special Bunsen burner, and suitable 
rubber tubing. 

The apparatus employed is shown in Fig. 24, in which 
R is the pressure regulator, M the gas meter, and C the 
calorimeter. A cross-sectional view of the calorimeter 
appears in Fig. 25. It consists of a combustion chamber 
A, in which the gas is burned at burner Q, surrounded by 
a water jacket B, which in turn is enclosed by an air 
jacket L to reduce radiation. The products of combustion 
pass down through a number of tubes within the water 
jacket and escape through the vent F, while the condensed 
water vapor formed by the combustion of the gas passes 
out through the outlet J. Water enters a small reservoir 
through pipe D and flows down tube E, through regulating 
valve V and tube F into the water jacket, thence out 
through tubes G and H into the measuring vessel W' 
(Fig. 24). The supply of water is adjusted so that some 
water alwaj^s flows over the reservoir and out the over¬ 
flow tube O, thereby maintaining a constant head of 
water. The temperatures of the water on entering and 
leaving the calorimeter are indicated by thermometers 
T' and T respectively, the temperature of the gas as it 
reaches the burner is given by thermometer T", and the 
temperature of the gaseous products of combustion is 
indicated by thermometer V". The damper Z is 
opened to provide sufficient draught for the flame. 

The pressu.e of the gas can be increased by placing 
weights in the form of disks upon the dome of the 
pressure regulator, each 22-gram disk augmenting the 
pressure by 2 mm. Hg. 

Procedure. After examining the apparatus to make 
sure that it is properly assembled, turn on the water 
at the faucet and increase its flow until it is sufficient to 
produce a continuous but moderate overflow. Remove 
the Bunsen burner, turn on the gas at the supply main, 
light the gas at the burner, and reclamp it properly in 


PHYSICAL LABORATORY EXPERIMENTS 77 


the combustion chamber. Caution —Never have the gas 
burning in the calorimeter unless water is flowing through 
the water jacket. Ad¬ 
just the flow of water 
through the calorimeter 
by means of valve V 
and the flow of gas to 
the burner by means 
of valve P so that the 
thermometers T" and 
T'" indicate approxi¬ 
mately the same tem¬ 
perature. After a 11 
thermometers indicate 
steady readings and 
when water drops from 
outlet J\ and at the 
instant when the large 
hand of the gas meter 
passes the zero mark, 
place collecting vessels 
W' and W in position 
to collect respectively 
the water from outlets 
H and J. Take simul¬ 
taneous readings of 
thermometers T and T' 
at one-minute intervals 
and when 9 liters of 
gas have been burned 
remove the collecting 
vessels. Measure the 
temperature of the con¬ 
densed water vapor 
collected in vessel W. 

Measure the mass of the water collected in each vessel. 
Perform the experiment a. second time, and thereafter 
turn off the gas and then the water. 








































78 PHYSICAL LABORATORY EXPERIMENTS 


Observations and Conclusions. Record all readings 
taken and arrange the data for the two determinations 
in parallel columns. From each test, calculate the heat 
of combustion of illuminating gas in calories per liter and 
in B.T.U. per cubic foot. Also reduce the first value to 
0° C. and 76 cm. Hg. pressure. 

EXPERIMENT 21 

Dew-Point and Humidity cf Atmosphere 

Object. To determine the hygrometric conditions of 
the atmosphere with the Daniell dew-point hygrometer 
and the wet- and dry-bulb psychrometer. 

Theory. The dew-point hygrometer consists of a 
vessel with an outer surface cf blackened glass or polished 
metal, and containing a liquid which may be cooled in 
various ways below the dew-point. The temperature of 
the liquid at which the water vapor in the atmosphere 
begins to condense in minute drops of water on the glass 
or metal surface is the dew-point. Having measured the 
dew-point and the temperature in any given locality, 
the relative humidity of the atmosphere at that place 
may be obtained by computing the ratio of the known 
pressures (Table XII) of saturated aqueous vapor at 
these temperatures, since the pressure is proportional to 
the quantity of vapor present. 

The psychrometer consists of two thermometers, one 
of which has its bulb surrounded by muslin that is kept 
saturated with water. When the instrument is placed 
in a current of air, the dry-bulb thermometer will indicate 
the temperature of the air, but the wet-bulb thermometer 
will indicate a lower temperature because of the evapora¬ 
tion of water from the muslin. The drier the air the more 
rapid will be the evaporation and therefore the greater 
the difference in the readings cf the two thermometers. 
The depression of the wet-bulb thermometer indication 
depends to some extent upon the velocity of ventilation, 
but if the air in the vicinity of the bulb moves at a velocity 


PHYSICAL LABORATORY EXPERIMENTS 79 


of 15 feet or more per second a constant maximum de¬ 
pression is attained. Under this condition the relative 
humidity up to temperatures of 140° F. may be com¬ 
puted by means of following formula, deduced by Pro¬ 
fessor Ferrel and employed as the basis of the Psychro- 
metric Tables used by the U. S. Weather Bureau; namely, 
that the pressure of the aqueous vapor actually present 
at the temperature t° F. is 

e = e' — Q.mmimt - ?) ( l + 

where e' is the maximum pressure of the vapor at the 
temperature t', H is the pressure of the atmosphere in 
inches of Hg., and t and t' are the temperatures in degrees 
F. of the dry- and wet-bulb thermometers respectively. 
If / be the maximum vapor pressure at the temperature t 
of the dry-bulb thermometer, then the relative humidity, 
expressed as a percentage, is 

1 1006 
k-— 

In these expressions, the pressures e, e! and / are expressed 
in inches of Hg., and the latter two quantities are ascer¬ 
tainable from Table XII. To find the dew-point, refer 
to this table of maximum vapor pressures and find the 
temperature corresponding to the value of e. 

The absolute humidity, or weight of aqueous vapor, in 
grains per cubic foot of the atmosphere at temperature t is 

352.4 6 

m ~ 30 ’l + 0.00204(* - 32)' 

where 352.4 is the density of water vapor in grains per 
cubic foot at 32° F. and at a pressure of 30 inches of Hg., 
and where 0.00204 is the coefficient of expansion of the 
vapor per degree F. 

Apparatus. Daniell dew-point hygrometer, ether, 
hygrodeik, barometer, and electric fan. 





80 PHYSICAL LABORATORY EXPERIMENTS 



Dew-point Hygrometer . The Daniell dew-point hygrom¬ 
eter consists of two glass bulbs joined by a bent tube 
and mounted on a stand as shown in Fig. 26.* The 
device contains ether, which is placed entirely in the lower 
bulb when a determination is made. The temperature 
of the ether is indicated by a thermometer enclosed in 
the lower bulb, and the temperature of the atmosphere 
is given by the thermometer at¬ 
tached to the stand. The upper 
bulb , is wrapped with a piece of 
muslin, and the lower bulb has a 
gilded rim on its surface. When 
ether is placed on the muslin, its 
evaporation cools the vapor within 
the bulb, some of the vapor con¬ 
denses and consequently the vapor 
pressure is reduced. This reduction 
of pressure in the lower bulb causes 
the evaporation of some of the ether 
and this process cools the lower 
bulb. In this way the temperature 
of the lower bulb gradually falls and the formation of 
dew on its outer surface may be observed. The appear¬ 
ance of moisture is best detected by moving a fine brush 
lightly across the gilded surface. The thermometers of 
the hygrometer used are graduated in degrees Reaumur; 
to convert to degrees F. multiply the reading by 2.25 and 
then add 32. 

Hygrodeik. The hygrodeik is a psychrometer having 
a graphic chart over which a pointer is free to imove. 
Two indexes are mechanically connected to the pointer, 
and when these indexes are adjusted along an auxiliary 
scale to indicate the readings of the two thermometers, 
then the position of the pointer on the chart shows 
directly the relative and the absolute humidity of the 
air as well as the dew-point. 

Procedure. Prior to using the Daniell hygrometer 
read both thermometers and derive the correction to be 


Fig. 26. 








PHYSICAL LABORATORY EXPERIMENTS 81 


applied to the exposed thermometer so as to agree with 
the other one. Then cool the ether in the lower bulb 
and note the temperature of the enclosed thermometer 
when dew appears. After cooling ceases and the tempera¬ 
ture again rises, note the temperature of the ether when 
the moisture on the gilded surface disappears. The 
mean of these temperature readings is taken as the dew¬ 
point. Observe the temperature of the atmosphere by 
means of the thermometer on the hygrometer stand. 
Make a second determination. 

Before wetting the muslin of the psychrometer ther¬ 
mometer, note the temperatures indicated by the two 
thermometers and deduce the correction to be applied 
to the dry-bulb thermometer in order to agree with the 
other. Then wet the muslin and place the hygrodeik 
in a current of air from the electric fan. When the wet- 
bulb thermometer indicates a steady reading, read both 
thermometers and the barometer. Set the indexes and 
pointer, and observe the humidity and dew point from 
the chart on the instrument. 

Take the hygrodeik out-of-doors and make a similar 
determination of humidity and dew-point at the new 
location. 

Observations and Conclusions. Record all data 
taken in tabular form for each instrument. Reduce 
the thermometer readings on the dew-point hygrometer 
to degrees F., and find the pressure of saturated aqueous 
vapor from Table XII at the dew-point and at corrected 
room temperature and compute the relative humidity. 
From the corrected thermometer readings on the hygro¬ 
deik compute the relative humidity, dew-point, and abso¬ 
lute humidity and compare the results with the direct 
indications on the chart of the instrument. 


£2 PHYSICAL LABORATORY EXPERIMENTS 


EXPERIMENT 22 
Thermal Conductivity of Metals 

Object. To measure the thermal conductivity of 
copper with Searle’s apparatus. 

Theory. One end of a metal bar is continuously 
heated by steam, while the other end is kept cool by 
water which flows in a steady stream through a helical 
tube wound around that end of the bar. If the rod 
were perfectly insulated so that no heat could escape 
from the sides of the rod, then the heat which travels 
along the rod when conditions become steady is the same 
at every cross-section, and when it reaches the cooling 
tube it raises the temperature of the flowing water from 
tj to t\° C. If m grams of the water are heated over this 
range every second, it follows that the heat traveling 
along the rod in calorics per second will be 


H = m(ti — to). 

The temperature gradient along the rod may be measured 
by placing thermometers in suitable thermal contacts 
located at two places on the rod. Let the temperatures 
at these contacts be t 2 and t 3 ° C., and the distance be¬ 
tween contacts be l cm. Then the temperature gradient 
in degrees C. per cm. is 

n t 3 — t 2 
G = ~[—- 

The thermal conductivity of the rod of cross-sectional 
area A sq. cm. is 



Apparatus. Searle’s conductivity apparatus, four 
thermometers, boiler, Bunsen burner, collecting vessel, 
graduate, and watch. 



PHYSICAL LABORATORY EXPERIMENTS 83 


The apparatus used for measuring the thermal con¬ 
ductivity of a particular sample of metal is shown in Fig. 
27. It consists of a cylindrical copper rod with a steam 
jacket at one end and a coil of several turns of small 
copper tube soldered around the other end of the rod 
This tube terminates in two small copper vessels in which 
are held the bulbs of the thermometers which measure 
the temperature of the entering and outflowing water. 
The thermal contacts for measuring the temperature 



gradient are small hollowed copper cylinders which are 
brazed to the bar. Thermometers fit loosely into these 
contacts and the space around the thermometer bulbs 
is filled with oil in order to provide good thermal con¬ 
tacts. The whole bar with its fittings is covered with 
felt so that the escape of heat from the sides of the bar 
is minimized. The diameter of the rod is 3.81 cm. and 
the distance between thermal contacts is 10.16 cm. 

Procedure. Light the gas at the Bunsen burner 
beneath the boiler and when steam is formed pass it 








84 PHYSICAL LABORATORY EXPERIMENTS 

through the steam jacket. Turn on the water through 
the cooling tube and regulate the rate of flow so that the 
temperature rise of the water will be at least 5° C. When 
each thermometer indicates a steady reading, collect the 
outflowing water in a vessel for a period of five minutes, 
taking readings of each thermometer at one-minute 
intervals during this time. Measure the amount of water 
collected with a graduate. Then change the rate of water 
flow through the cooling tube and take similar observations 
for another five-minute period. Thereafter turn off gas 
and water. 

Observations and Conclusions. Arrange the tem¬ 
perature readings in parallel columns and compute the 
average indication of each thermometer for each of the 
two tests. Thereafter calculate for each test the dis¬ 
charge of water in grams per second, the flow of heat in 
calories per second, the temperature gradient along the 
copper rod, and the thermal conductivity of copper. 
Compare the value of k obtained by experiment with the 
values given in Table XIII. 


EXPERIMENT 23 
Refractive Index cf Prism 

Object. To measure the angle of a glass prism and to 
determine its index of refraction for sodium light by means 
of a spectrometer. 

Theory. Let a ray of light from a point source be 
reflected from one face of a prism to a definite point. 
Then move the prism through a measured angle so that 
a ray from the same source will be reflected from the 
second face of the prism to the same reference point. 
If the angle through which the prism was turned be 0 
degrees, then the angle of the prism between the two 
faces referred to will evidently be 


<i> = 180° - 0. 


PHYSICAL LABORATORY EXPERIMENTS £5 


Consider a beam of monochromatic light incident upon 
one face of a prism at an angle i to its normal. The beam 
will enter the prism and make an angle r with this nor¬ 
mal and will then pass out of the second face of the prism, 
making angles of incidence i' and refraction r' with the 
normal to the second face. From geometric considera 
tions, the angle of the prism is 


$ = r + i'j 


and the angle of deviation between the incident and 
emergent rays will be 

D = i - r - H + r '. 


Since sin i = \x sin r, and sin i' = - sin r', where m is the 

index cf refraction cf the prism (relative to air), it follows 
that 

D = sin -1 (/x sin r) — + sin -1 (/z sin [<I> — r]). 


In order to find the relation between r and i f which will 
make the angle of deviation a minimum, differentiate 
the foregoing expression with respect to r and then equate* 
the result to zero and solve. Thus 


dD 

dr 


/jl cos r 


r 


_ ju cos (3> — r) 

A / 1 _ ..2 0^2 . 


= = 0 


whence 

cos 2 r _ 1 — /z 2 sin 2 r 
cos 2 i' ~ 1 — i u 2 sin 2 i 1 


and it follows that r = i'. Consequently the minimum 
deviation of the beam in passing through the prism 
occurs when the angles r and i' are equal, whereby angles 
i and r' are also equal. Then the angle of minimum devia¬ 
tion will be 


D m = 2 (i - r) 








86 PHYSICAL LABORATORY EXPERIMENTS 

and the refractive index of the transparent material form¬ 
ing the prism is 

__ sin i _ sin f (3> -f- D m ) 
sin r sin 

Apparatus. Spectrometer, prism, combined fish-tail 
and Bunsen burner, and sodium bead on platinum wire 
supported on burner. 

The spectrometer comprises an accurately graduated 
circular scale, a movable horizontal table, a collimator 
carrying a slit of adjustable width, and a telescope for 
viewing the slit, all mounted upon a base. The scale, 
table and telescope are constructed so that they may be 
moved about a common vertical axis, and are severally 
equipped with clamping screws for holding them in any 
desired position. The telescope is provided with cross¬ 
hairs, and its mounting carries a tangent screw for secur¬ 
ing fine adjustment in locating the telescope, and a pair 
of verniers 180° apart for reading its position on the 
graduated circle. The instrument has been adjusted so 
that the optic axes of telescope and collimator are per¬ 
pendicular to and intersect the vertical axis of the instru¬ 
ment. Before using the spectrometer for angular meas¬ 
urements, two adjustments must be made, namely: to 
focus the telescope, and to focus the collimator. 

To focus the telescope, look through the telescope 
toward some bright object and adjust the position of 
the eye-piece so that the cross-hairs are in distinct focus. 
Then focus the telescope proper upon some distant 
object until its image lies in the plane of the cross-hairs 
as evidenced by lack of parallax, the eye-piece adjustment 
remaining unaltered. 

To focus the collimator, place the telescope coaxial 
with the collimator, and place an illuminating flame 
back of the collimator slit. Look through the telescope 
and bring the image of the narrow slit into sharp focus 
and without parallax with the cross-hairs. This adjust¬ 
ment must be made by moving the slit toward or away 



PHYSICAL LABORATORY EXPERIMENTS 87 


from the collimating lens while leaving the original 
adjustment of the telescope unaltered. 

Procedure. Carefully examine the graduations on 
the scale and verniers, and become familiar with the 
methods of coarse and fine adjustment of the spectrom¬ 
eter. Be sure to release the clamping screw of any 
part of the instrument that is to be shifted before attempt¬ 
ing to move that part. Focus the telescope and colli¬ 
mator for parallel rays as already explained. 

Angle of prism. To measure the angle of the prism 
clamp the telescope at an angle of approximately 60° 
with the collimator, and clamp the table to the graduated 
circle, which is left free to turn. Place the prism centrally 
on the spectrometer table and adjust the leveling screws 
on the table until the faces of the prism are vertical. 
Set the slit in a vertical position and illuminate it with 
the fish-tail burner. Then turn the table with prism 
so that the beam of light from the slit will be reflected 
from one face of the prism and enter the telescope, 
forming an image of the slit upon the vertical cross-hair. 
Determine this position of the prism by reading both 
verniers. Rotate the prism and scale until a similar 
reflection from the second face of the prism is obtained, 
and note its new position by reading both verniers. These 
observations provide the data for computing the refract¬ 
ing angle of the prism. 

Angle of minimum deviation. To measure the angle of 
minimum deviation clamp the scale to the collimator, 
but release the knurled screw which clamps the spectrom¬ 
eter table to the graduated circle. Unclamp the tele¬ 
scope and move it into such position that, with the prism 
removed from the spectrometer table, the image of the 
slit will be received upon the vertical cross-hair of the 
telescope. Then read both verniers. Form a sodium 
bead at the bent end of a platinum wire which is sup¬ 
ported in the hood of the burner. Adjust the hood so tha, 
the bead touches the Bunsen flame just above the burner, 
the burner being located about three inches back of the 


88 PHYSICAL LABORATORY EXPERIMENTS 

collimator slit. Place the prism on the spectrometer 
table and rotate the telescope to receive the light from 
the collimator after being refracted through the prism. 
Turn the prism slowly and follow the image of the slit with 
the eye until the angle between the refracted ray and the 
prolonged collimator axis is a minimum. Then bring 
the telescope into position and watch the slit image in 
the telescope while slight movements of the prism are 
made. Adjust the prism to the position for which the 
deviation of the refracted ray is least and then move the 
telescope with the tangent screw so that its vertical 
cross-hair will bisect the image of the slit. After verify¬ 
ing this adjustment of the telescope by turning the prism 
slightly in each direction, take readings of both verniers. 
The data for obtaining D m for sodium light are now at 
hand. 

Observations and Conclusions. Call one vernier 
A and the other B. Record all spectrometer readings 
in tabular form, placing the observations taken on the 
two verniers in parallel columns bearing the captions: 
Vernier A, and Vernier B. Compute the arithmetical 
mean value of 6 and of D m as given by the two verniers, 
in order to correct for eccentricity due to the non-coin¬ 
cidence of the axes of rotation of the graduated circle 
and the telescope. Determine the angle of the prism 
and then calculate the refractive index for sodium light 
of the glass of which the prism is constructed. 

EXPERIMENT 24 
Focal Lengths of Convex Lenses 
Radius of Curvature of Concave Mirror 

Object. To determine the focal length of a thin 
converging lens by two methods, the focal length of a 
thick lens, and the radius of curvature of a concave 
spherical mirror by two methods. 


PHYSICAL LABORATORY EXPERIMENTS 89 

Theory. An object is placed before a thin converging 
lens at a distance away greater than the focal length 
of the lens. A real inverted image of this object will be 
formed on the other side of the lens, the usual construc¬ 
tion lines being shown in Fig. 28. Let the distances 
from the center of the lens to the object of length 0, 
to the image of length 7, and to either focus F be called 








<— f _^ 

a -* 

< - V 

J 


Fig. 28. 


P, q and / respectively, 
figure 

0 _ p 

whence 


Then from the geometry of the 

0 _ / 


and 


Q-f 


/ = 


M 

p + q 


The focal length of a thin converging lens may be 
determined with the use of this equation in two ways: 
(1) by measuring the object distance p and the corre¬ 
sponding image distance q and substituting these values 
in the formula, and (2) by choosing an object at a great 
distance so that p may be considered infinite, and measur¬ 
ing the image distance q, which is then equal to/. 

With a thick lens or a lens combination the object 
and image distances cannot be measured from its geo¬ 
metric center nor from the lens surfaces. However, 
the focal length of such lenses can be determined experi¬ 
mentally with sufficient accuracy by finding the dis¬ 
tance between the two positions of the lens at which 
distinct images are obtained for a fixed distance between 
















90 PHYSICAL LABORATORY EXPERIMENTS 


object and image. If the lens must be moved a distance 
a from one of these positions to the other, and the dis¬ 
tance between the object and image be l, then 

a = q — P and l = q + p. 

Substituting the values of p and q herefrom in the fore¬ 
going expression for /, there results 

l 2 - a 2 
J 4 1 * 

The radius of curvature of a concave mirror can also 

VQ 

be obtained from the equation f = -if it be remem- 

P + Q 

bered that parallel light incident near the vertex of such 
a mirror will be reflected to the focal point midway 
between the vertex and the center of curvature of the 
mirror. Thus, the radius of curvature r — 2/, whence 

■ r _ 

V + <1 

Two methods of experimental procedure suggest them¬ 
selves: (1) to measure the object distance p and the 
corresponding image distance q and substituting the values 
in the equation for r, and (2) to place the object in such 
position that the image will coincide with it, in which 
case p = q, and consequently r = p = q. 

Apparatus. Optical bench graduated in mm., thin 
converging lens, lens combination, concave mirror, plane 
mirror, white screen, straight-filament incandescent lamp, 
and mounted needle point. 

The straight-filament incandescent electric lamp serves 
as the object in the measurements of focal length of lenses 
and in one of the methods employed for determining the 
radius of curyature of the concave mirror. The lamp, 





PHYSICAL LABORATORY EXPERIMENTS 91 


lens and screen are mounted on separate carriages which 
may be moved along a 2-meter graduated optical bench. 

Procedure and Observations. Thin lens. (1) Place 
the screen at distances varying from 130 to 200 cm. 
from the illuminated lamp at intervals of 10 cm., and for 
each setting adjust the lens at an intermediate position 
on the optical bench which will yield a distinct image of 
the object (lamp) on the screen. Note the distance from 
the lamp to the lens, p , and the distance from the lens 
to the screen, q, for each test, and place the readings in 
tabular form. Reserve one column in the table for cal¬ 
culated focal lengths. 

(2) Replace the lamp by a mirror and adjust it to 
such an angle that a ray of sensibly parallel light from 
some distant object will be reflected onto the lens. Move 
either the lens or the screen until a sharply defined image 
of the distant object is projected on the screen. Measure 
the distance between the lens and screen. Repeat the 
adjustment and take another observation. 

Lens combination. Interpose the lens combination be¬ 
tween the illuminated lamp and the screen, and vary the 
distance from lamp to screen from 100 to 130 cm. in steps 
of 5 cm. For each setting locate the two positions of 
the lens on the bench which yield distinct images of the 
lamp filament on the screen, and note the distance be¬ 
tween these positions. Record observations in tabular 
form, and reserve a column for the values of focal length 
to be calculated. 

Concave mirror. (1) Place the mirror with its stand 
near the illuminated lamp and shift the screen until 
a well-defined image of the filament is obtained. The 
adjustment may be made more accurately if the mirror is 
partially covered so that only the portion near its vertex is 
exposed. Measure the distances from the mirror to the 
lamp and to the screen. Then make another independent 
setting and record results. 

(2) Set the mounted needle point as object before the 
mirror and place the eye in the prolonged line through 


92 PHYSICAL LABORATORY EXPERIMENTS 


the needle point and vertex of mirror. Adjust the posh 
tion of the needle along the line of vision until no parallax 
between object and image is evident when moving the 
eye to either side; the needle is then at the center of 
curvature of the mirror. Measure the distance from 
the vertex of the mirror to the needle point. Repeat 
the adjustment, and take another observation. 

Conclusions. Compute from the observations taken 
the average focal length of the thin lens by both methods, 
the average focal length of the lens combination, and the 
average radius of curvature of the concave mirror by 
both methods, all results being expressed in cm. 


EXPERIMENT 25 


Calibration of Ocular Scale of Cathetometer 


Object. To calibrate the eye-piece scale of a cathe¬ 
tometer microscope with a standard scale, and to de¬ 
termine the ratio of the centimeter to the inch. 

Theory. In this experiment the eye-piece of the cathe¬ 
tometer microscope is adjusted to yield an image of the 
transparent ocular scale at the distance of distinct vision, 
and the objective is adjusted to produce an image (with 
the aid of the eye-piece) of the standard scale at the 
same distance, so that both scales will be seen through 
the microscope superimposed upon each other. By 
observing the number of divisions on ohe ocular scale 
which is subtended by some integral number of divisions 
on the standard scale, the calibration of the ocular scale 
is effected. If S ocular divisions are subtended by L 
cm. on the standard scale, the value of an ocular division 


will be ^ cm. 

o 


Apparatus. Cathetometer with ocular scale, stand¬ 
ard steel cm. and inch scales, and holder for standard 
scale. 


PHYSICAL LABORATORY EXPERIMENTS 93 


The cathetometer consists of a horizontal microscope 
mounted on a vertical stand so that its axis may be 
raised or lowered. The height of an object can be 
measured accurately by the cathetometer by focus¬ 
ing the microscope successively at the top and the 
bottom of the object and noting the difference of the 
elevations of the microscope in the two positions by 
means of a vernier moving along a vertical scale. Very 
small vertical distances may be measured by means 
of the ocular scale without moving the microscope, 
after this scale has been calibrated. 

Procedure. Mount the standard centimeter scale 
in a vertical position and place the cathetometer a 
short distance away and level its microscope. Remove 
the eye-piece of the microscope and focus it so the 
divisions on the image of the ocular scale will appear 
clear and distinct. Replace the eye-piece with its 
scale vertical and then adjust the length of the micro¬ 
scope draw tube to division 13 on the tube scale. Then 
focus the microscope on the standard scale by moving the 
entire microscope back and forth by means of its twin 
knurled screws. A correct focus is indicated by the 
absence of parallax, that is, the lack of relative move¬ 
ments of the images of the two scales when the eye 
is moved vertically before the eye-piece. Determine 
the number of divisions on the ocular scale that is sub¬ 
tended by the largest integral number of divisions of 
the standard scale visible over the range of the ocular 
scale. Increase the length of the tube in steps of 1 cm. 
up to its limiting length, and at each setting take a read¬ 
ing as before. 

Replace the cm. scale by a standard inch scale and 
make another set of observations in the manner described. 

Observations and Conclusions. Evaluate the 
length of a division of the ocular scale for each tube 
setting, both in cm. and in inches. Put these values 
together with the observations in tabular form. Plot 
a curve with tube lengths as abscissas and with the 


94 PHYSICAL LABORATORY EXPERIMENTS 


values of an ocular division (that is, L/S) in cm. as 
ordinates. For each tube length find the ratio of the 
values of L/S determined on the inch and cm. standard 
scales. The average value of this ratio gives the number 
of cm. in one inch. 

EXPERIMENT 26 

Curvature of Cornea of Eye with Ophthalmometer 

Object. The measurement of the radii of curvature 
of the anterior surface of the cornea at various axes and 
the determination of corneal astigmatism of the human 
eye by means of the Javal-Schiotz ophthalmometer. 

Theory. Astigmatism is the most common of the 
refractive errors of the human eye, and is due almost 
entirely to asymmetry of the cornea. The curvature of 
the cornea of an astigmatic eye has different values at 
various meridians, the two meridians giving the max¬ 
imum and minimum refraction at the corneal surface 
being termed the chief meridians. These meridians are 
at right angles to each other, but are not necessarily 
horizontal and vertical respectively. The vertical (or 
more nearly vertical) chief meridian of the cornea has 
usually the maximum and the other meridian the mini¬ 
mum of curvature; when this is the case, it is spoken 
of as astigmatism with the rule, and when the reverse is 
true it is called astigmatism against the rule. 

The ophthalmometer is an instrument for observing 
the positions of the images of two illuminated objects 
formed by reflection from the surface of the cornea, 
which acts as a convex mirror. The eye to be observed 
is placed at the center of a horizontal arc along which 
the luminous objects or mires may be moved so as to 
alter the distance between them. This arc is rotatable 
about a horizontal axis coincident with the optic axis 
of the eye in order to bring the mires into any corneal 
meridian. If the distance between the mires be deter¬ 
mined as well as the distance between their images 


PHYSICAL LABORATORY EXPERIMENTS 95 


formed by the cornea, then the corneal curvature may 
be computed. 

In Fig. 29, EE is the anterior surface of the cornea, 
so placed that it is concentric with the arc AHB, upon 
which are supported the mires M and N. The inner edges 
of these mires will be taken as the reference points and 
the distance between the edges, AB, will be considered as 
the size of the object. Three rays from A are incident 



upon the cornea at the points a, a' and a", where they 
are reflected to A, R and S respectively. Likewise 
three rays from B are incident upon the cornea at b, 
b' and b", where they are reflected to B, S and R re¬ 
spectively. The two groups of reflected rays appear to 
come from the points A' and B' back of the reflecting 
surface, and these points are the inner edges of the vir¬ 
tual images M' and N' of the two mires. The distance 
between A' and B' will be the size of the image. 

Fig. 29 is not drawn to scale, but some parts are 








96 PHYSICAL LABORATORY EXPERIMENTS 


magnified and others reduced in order to attain clearness. 
In the opththalmometer the radius CH of the arc AB 
is about 35 times as large as the radius r of the cornea. 
Consequently the object AB may be considered very 
remote and the image A'B' will practically be at the 
principal focus F of the cornea, which lies midway be¬ 
tween its vertex J and center of curvature C. If the 
sizes of object and image be respectively 0 and I, and 
if their distances from the cornea be respectively d and 

then 

0 _d+r _2l+r 

7 r 
2 

where l is the distance between object and image; whence 
the radius of curvature of the cornea is 

211 



Fig. 30. 


The measurement of the size of the image I is accom¬ 
plished by viewing the images of the mires by a telescope 
containing a Wollaston bi-refringent quartz prism, and 
shown diagrammatically in Fig. 30. The prism B, 
placed between the similar achromatic lenses A and C, 
is a rectangular parallelopiped consisting of two sim¬ 
ilarly shaped triangular prisms, so cut that in one the 
axis of the crystal is perpendicular to the apex of the 
triangle and in the other parallel thereto. The rays 
from each mire, after reflection from the cornea, enter 
the prism where they are separated into two sets a and 















PHYSICAL LABORATORY EXPERIMENTS 97 


b, the extraordinary and ordinary rays. These rays are 
brought to a focus and two images are formed of each 
mire at the focal plane D, where the images are viewed 
by an eye-piece. Since the lenses A and C have the 
same focal length, and since lens A is oriented so that 
its principal focal plane coincides with the image back 
of the cornea (A'B' of Fig. 29) the size of this image 
will be reproduced by lens C in the focal plane at D. 
The separation of the two images of each mire by the 
prism, or the amount of doubling, in the Javal-Schiotz 
ophthalmometer is 3 mm., and remains constant irre¬ 
spective of the separation of the mires. In use, the mires 
of this ophthalmometer are shifted until the ordinary 
image of one mire, as seen through the telescope, touches 
the extraordinary image of the other mire, in which case 
the size of the image I = 0.3 cm. Then, since the dis¬ 
tance l in this instrument is 27 cm., the radius of curva¬ 
ture of the cornea under examination is given directly as 


2X27X0.3_ 16.2 
0-0.3 0-0.3' 


Thus, if the mires were separated 20.5 cm., in order 
to have their images touch for a certain eye, then the 


radius of curvature of its cornea would be 


16.2 

(20.5-0.3) 


or 0.8 cm. 

Apparatus. Javal-Schiotz ophthalmometer, indicat¬ 
ing lens tester, and cm. scale. 

The construction of the ophthalmometer is indicated 
in Fig. 31. It consists of a head-rest with an adjust¬ 
able chin-piece, of two mires which can be moved apart 
along a circular arc by means of spiral tracks upon the 
front face of a dial, of a telescope containing the bi- 
refringent prism and lenses and equipped with rack and 
pinion as well as an elevating arrangement for bringing 
either eye of any subject into focus, and of a scale on 
the rear face of the dial for indicating directly by the 





98 PHYSICAL LABORATORY EXPERIMENTS 


use of suitable pointers the inclination of the mire arc, 
the radius of curvature of the cornea, and its astigmatism 
expressed in diopters. The mires are illuminated by 
miniature electric lamps and are of dissimilar shape, 
one is a rectangle and the other is a figure consisting of 
steps, both mires being divided into halves by black 
lines. When the rays from the mires after reflection 
from the cornea are viewed through the telescope, two 
images of each mire will be observed and will appear 
as in Fig. 32 for the horizontal and vertical positions 



Fig. 31. 


of the mire arc, P and Q representing the ordinary and 
P' and Q' the extraordinary images. Only the two 
central images, namely P' and Q, are considered in making 
a determination of corneal astigmatism. 

Fig. 32 for the horizontal position shows that the 
mires were so moved that the inner edges of the images 
P' and Q touch, indicating that the size of the image I 
( A'B' in Fig. 29) is 0.3 cm. Assuming that the cornea 
is astigmatic with the rule, then, when the mire arc is 
turned 90 degrees to the position shown at the right of 
Fig. 32, it will be found that the images P' and Q over¬ 
lap, the white portion of image Q representing the 


PHYSICAL LABORATORY EXPERIMENTS 99 


amount of overlap. In this case the radius in the ver¬ 
tical meridian is less than in the horizontal, and there¬ 
fore the size of image I is decreased. In order to make 
7 = 0.3 cm. in the vertical position it is necessary to 
move the mires until the images P' and Q just touch. 
The radius of the cornea in either meridian is then 
readily determined from the corresponding separation 0 
of the inner mire edges by means of Equation (1). The 




MIRES HORIZONTAL 


.m 

HIRES VERTICAL 

Fig. 32. 


rear of the ophthalmometer dial is graduated in accord¬ 
ance with this equation so that when the disk is turned in 
the process of moving the mires until their images touch, 
the radius of curvature of the cornea will be indicated 
directly in mm. against an index. 

The principal focal distance, f cm., of a lens constructed 
of material having a refractive index ju and having radii of 
curvature r and ri cm. is given by the usual lens formula 


r ri 














100 PHYSICAL LABORATORY EXPERIMENTS 
For a plano-convex lens r\ becomes infinity, and therefore 



Considering the cornea of radius r to be merely the 
transparent shell of the aqueous humor of refractive 
index 1.337 (see Table XV), the refractory power of the 
cornea expressed in diopters is 



1.337-1 33.7 


( 2 ) 


r 


r 


Thus, when the radius of curvature of the cornea in 
the horizontal meridian is 7.5 mm., and in the vertical 
meridian is 7.0 mm., then the refractory power of the 
cornea in the two meridians is 33.7^0.75 = 45 diopters 
and 33.7-^0.7 = 48.1 diopters, and the astigmatism is 
48.1-45.0 = 3.1 diopters “with the rule.” The dial 
of the ophthalmometer also carries a dioptic scale grad¬ 
uated in accordance with Equation (2), so that the 
refractory power of the cornea can be read directly at 
either axis. 

Procedure. Seat the individual whose eyes are to 
be tested in position so that the upper part of the head¬ 
rest is just above his brows, adjusting the chin-rest 
by means of the horizontal milled screw at the rear 
of the ophthalmometer. Obstruct one eye with the 
shutter and by looking through the sight holes in the 
dial align the telescope with the other eye. Illuminate 
the mires. Adjust the eye-piece of the telescope by 
turning it so that the cross-hairs may be viewed free 
from parallax. Find the mire images in the telescope 
by raising or lowering it with the use of the vertical 
milled screw and by swinging it to right or left, as re¬ 
quired, in order to bring the two central images at the 
intersection of the cross-hairs. Focus the telescope by 
means of the milled wheel at its side until the images are 
seen distinctly; do not alter this adjustment throughout 



PHYSICAL LABORATORY EXPERIMENTS 101 

the measurement of this eye. Locate the primary axis 
by grasping the telescope at the leather-covered tube 
and turning it, not more than 45 degrees either side of 
the zero mark, until the continuity of the two central 
black lines through the mires is established. Then bring 
the mires together until their edges just touch by re¬ 
volving the dial with the aid of the capstan pins. Finally 
move the pointer with the extension hook directly back 
of the other pointer so as to be covered by it. 

Revolve the telescope through the zero mark to the 
secondary position which is just 90 degrees from the other 
chief meridian, and it will be observed that the black 
lines through the mires again lie in one line. If the eye 
under examination is astigmatic, the mire images will 
appear overlapped or separated. Then adjust the mires 
by turning the dial so that their images again touch. 
It will now be observed that the two pointers occupy 
different positions on the dioptic scale, and the dif¬ 
ference between them is the astigmatism in diopters, 
and the axes of the two chief meridians are indicated 
on the small disk. 

Observations and Conclusions. Verify the accu¬ 
racy of the scales on the ophthalmometer dial by meas¬ 
uring the distance 0 between the inner edges of the 
mires and using Equations (1) and (2). Test the right 
eye (0. D.) and the left eye (O. S). of one member of the 
group performing this experiment. Record these read¬ 
ings and add those taken on your own eyes. If you 
wear glasses measure the curvature and cylindncity of 
each spectacle lens by means of the indicating lens 
tester. Place the observations on the four eyes in 
tabular form and indicate the names of the individuals 
concerned in the tests. Determine the amount, the 
principal meridians and the nature of the astigmatism of 
your eyes and state the extent to which your glasses 
remedy this defect of vision. 


102 PHYSICAL LABORATORY EXPERIMENTS 


EXPERIMENT 27 

Magnifying Power of a Compound Microscope 

Object. To determine the magnifying power of a 
compound microscope by calculations based upon its 
tube length and upon the trade markings on its objective 
and eye-piece, and to verify this result by direct experi¬ 
ment. 

Theory. The optical elements of a compound mi¬ 
croscope are an objective, made up of several lenses and 
having a short focal length, and an eye-piece, generally 
made of two lenses and also having a short focal length. 
A strongly illuminated object, often in the form of a slide, 
is placed just a little distance beyond the principal 
focus of the objective. The objective forms a real 
magnified image of the object in space on the other 
side and some one or two hundred millimeters away from 
the objective. This magnified real image is viewed by 
an observer through the eye-piece just as though he were 
using an ordinary simple magnifying glass. The image 
which he sees is at the distance of distinct vision, usually 
250 millimeters. 

To determine the magnification produced by the ob¬ 
jective, that is, the ratio of the distance between two 
points of the image to the distance between the corre¬ 
sponding points of the object, one may rely upon the 
relations expressed by the ordinary lens formula: 

-+- = i .... (Exp. 24) 
P q f ' 

wherein p and q represent respectively the distances of the 
object and image from the lens and / is the principal 
focal length of the lens. In order to make use of this 
formula, consideration must be given to the great axial 
thickness of the lens combination which constitutes the 
objective. On the axis of a thick lens there are two 
particular points which are termed the first and second 
principal points, and these points are usually close 


PHYSICAL LABORATORY EXPERIMENTS 103 


together. Were an object placed in a plane passed 
perpendicular to the axis through the first principal 
point, an image would be formed in a similar plane 
passed through the second point and it would be of 
the same size as the object, consequently the magni¬ 
fying power will be unity. If, now, the distance of some 
remote object be measured from the first principal 
point and the distance of the resulting image from 
the second principal point, then the ordinary lens formula 
just given applies as well to thick as to thin lenses. 
The principal focal length must similarly be measured 
from the focus of parallel rays to the principal point 
on the same side of the lens as this focus. When so 
measured the two principal focal lengths on opposite 
sides are numerically equal to each other. This length 
is usually indicated upon the mountings of microscope 
objectives. 

Since, in using the microscope the object is placed 
just slightly beyond the principal focus, the object dis¬ 
tance may be considered as equal to the focal length 
/. In order to cut off extraneous light, the rays which 
extend from the objective to the magnified real image 
of the object are enclosed in a light-tight tube and the 
distance T from the image to the second principal point 
is termed the optical tube length. The corresponding 
linear dimensions of the image and object will vary 
directly as their distances from their respective prin¬ 
cipal points. The magnification produced by the ob¬ 
jective may therefore be taken as 



The magnification produced by the eye-piece of focal 
length /' millimeters is in accordance with the usual 
expression: 


250 


104 PHYSICAL LABORATORY EXPERIMENTS 


When the eye-piece is used for viewing the image pro¬ 
duced by the objective, the total magnification is equal 
to the product of m Q and m e , or 


m = m 0 m e = 


2507 7 
//' ’ 


( 1 ) 


all dimensions being in millimeters. 

Eye-pieces usually consist of two lenses, the magni¬ 
fying lens in the end toward the observer’s eye, and 
a field or collective lens which enables the observer to 
view a large field and to secure simultaneous focus of 
the central and peripheral portions of the field. They 
are usually stamped with a numeral indicating their 
magnifying powers used simply as a magnifier and often 
with equivalent focal length, that is, the focal length 
of a thin lens which would have the same magnifying 
power. Within these eye-pieces is a diaphragm so lo¬ 
cated that when the microscope is focused the real 
image produced by the objective and aided by the 
field lens will be formed at this diaphragm. The optical 
tube length is then the distance between this diaphragm 
and the second principal point of the objective. It is 
the present practice to have this latter point located in 
the plane of the flange of the mounting of the objective, 
as at A, Fig. 33 (this plane passes through the upper 
point of the letter A). The equivalent focal length of 
eye-pieces for magnifying powers of 5, 10 and 15 are re¬ 
spectively 50, 25 and 16.7 millimeters. 

If the magnifying powers m\ and m 2 of a microscope 
with two unknown optical tube lengths T\ and T 2 , 
whose difference, however, may be measured on the 
draw tube scale, be experimentally determined, then, 


since, m\ = 


2507T 
//' ’ 


and m 2 = 


250T 2 
//' ’ 


it follows that 


//r _ 250 {T 1 -T 2 ) 


mi —m2 


( 2 ) 








PHYSICAL LABORATORY EXPERIMENTS 105 


Substituting; this value of ff' in the equations for mi 
and m 2 yields 

Ti = an d t 2 = m2( - Tl ~ T2 \ 

mi —m 2 m\ —m 2 

Apparatus. A compound microscope with one ob¬ 
jective and one eye-piece, a stage micrometer slide ruled 
to 0.01 mm., a millimeter 
scale, an illuminating arc- 
lamp with rheostat, a draw¬ 
ing board with light shield 
and attached stand for hold¬ 
ing the microscope. 

The microscope, Fig. 33, 
consists of a base B, pillar 
P, stage S, and handle-arm 
H, to the last of which is 
attached by a rack and 
pinion the microscope tube T. 

Within this tube there is 
movably fitted the graduated 
draw tube D, in whose upper 
end is placed the eye-piece E. 

To the lower end of the 
body tube is fastened a 
rotatable nose piece N into 
which is screwed the objec¬ 
tive 0. Rays of light from 
the source of illumination 
are reflected by the universally movable mirror M, 
through the condenser in the substage S' upon the 
stage micrometer slide placed directly under the ob¬ 
jective. In use, the upper portion of the microscope 
with the stage will be turned through 90 degrees around 
the inclination joint I, and will then be mounted upon 
the extension of the drawing board as shown in Fig. 
34. The arc light connected in series through the rheo- 



Fig. 33. 























106 PHYSICAL LABORATORY EXPERIMENTS 


stat to the electrical supply mains is adjusted to send 
light upon the mirror M , which redirects it through 
the tube. When properly focused a real image will 
be formed upon a sheet of paper lying on the drawing 
board. Fig. 35 shows the microscope fitted with a 
micrometer eye-piece for measuring distances on the 
object viewed by the microscope. 

Procedure. Connect the arc light in series with 
the rheostat to the 110- volt service mains, the carbons 
being originally separated. Then turn the regulating 



Fig. 34. 


screws of the lamp until the carbons just make contact 
and then immediately separate the carbons a short dis¬ 
tance (if the carbons be left in contact, the rheostat is 
likely to become injured). Direct the rays of the lamp 
upon the microscope mirror at right angles to the axis 
of the microscope tube, which has been mounted as 
shown in Fig. 34. Then adjust the mirror so as to send 
the reflected rays from the lamp through the tube. 
Adjust the tube length so that the distance from the 
flange of the objective mounting to the eye-piece end of 
the draw tube is 160 mm. Place a sheet of paper upon 
the drawing board and focus the stage micrometer image 





PHYSICAL LABORATORY EXPERIMENTS 107 



Fig. 35. 


108 PHYSICAL LABORATORY EXPERIMENTS 


upon the paper. In focusing the microscope the tube 
should be at first lowered carefully until the objective 
just clears the object, and then, while looking through 
the instrument, the tube should be gradually withdrawn 
by turning the pinion head P (Fig. 33) until the object 
becomes visible, after which the micrometer head M' 
should be used to obtain a sharp focus. Great care 
should be taken with objectives, which are made of 
soft glass, so as not to scratch their surfaces by coming 
in contact with the object observed. 

Mark upon the paper two lines corresponding to two 
divisions of the image which are separated by 100 
divisions. The distance between these marks corre¬ 
sponds in the image to one millimeter in the object. 
Measure this distance in millimeters, and the result is 
the magnifying power for this tube length. Then in¬ 
crease the tube length by a measured number of milli¬ 
meters, say 40 or 50, which distance can be read off 
the scale on the draw tube. Then repeat the process 
and determine the new magnifying power. Finally 
remove the eye-piece and, after unscrewing the eye lens, 
measure the distance in millimeters from the diaphragm 
to the upper edge of the eye-piece mounting. 

Observations and Conclusions. Record all meas¬ 
urements in tabular form, and also note the markings of 
equivalent focal length on objective and eye-piece. From 
these markings and from the measured optical tube length 
compute the magnifying power of the microscope from 
Equation (1). Compare this value with the magnifying 
power as observed by test for the same tube length. Then 
calculate from the measurements of magnifying power 
for two different tube lengths the value of the product 
of the focal lengths of objective and eye-piece by using 
Equation (2), and compare this product with that result¬ 
ing from the maker’s ratings on these parts. (Manu¬ 
facturers of microscopes guarantee focal length ratings 
to be accurate to 2 per cent.) Also calculate the values 
of optical tube lengths for the two settings of the draw 


PHYSICAL LABORATORY EXPERIMENTS 109 


tube and compare them with the distances between the 
eye-piece diaphragm and the flange of the objective 
mounting for the same settings. 

EXPERIMENT 28 

Wave-lengths of Light by Interferometer 

Object. To measure the wave length of sodium light 
by means of the Michelson interferometer. 

Theory. The Michelson interferometer consists of 
two parallel-sided glass plates of equal thickness, shown 





at A and B of Fig. 36, and two plane mirrors, shown 
at M and M'. The glass plate A is half-silvered on 
the face marked s, so that an incident beam of light 
from a luminous source S will be divided into two beams, 
one of which is reflected to mirror M and the other is 
transmitted to mirror M'. After reflection at their 
respective mirrors, these beams are returned along their 
initial path and pass through plate A to the observer 
at 0. The clear glass plate B is introduced between 









110 PHYSICAL LABORATORY EXPERIMENTS 


A and M so that both beams will pass through the same 
thickness of glass. When the two mirrors are exactly 
perpendicular to the beams of monochromatic light 
incident thereon, and when the mirrors are located 
at precisely equal distances from the half-silvered plate, 
then the two beams upon reunion at 0 are in condition 
to interfere, because of their opposition in phase occa¬ 
sioned by the dissimilar reflections at A. Should mirror 
M' be moved perpendicularly to itself a distance of 
one-half wave-length, the reunited beams will again 



Pig. 37. 


interfere, since the path from A to M' and back to A 
has been increased by a full wave-length. At such 
interferences the field of view at 0 will appear dark, 
while midway between them the field will be illumi¬ 
nated. If mirror M' be moved slowly in one direction 
over a distance l cm., while the number n of darkenings 
of the field be counted, then the wave-length of the 
monochromatic light used will be 



— cm. 
n 


PHYSICAL LABORATORY EXPERIMENTS 111 

Apparatus. Interferometer attached to a micrometer 
slide which is mounted in a heavy adjustable support, 
sodium burner, and observing telescope. 

The interferometer is illustrated in Fig. 37, which shows 
the two glass plates firmly mounted on a metal plate. 
The fixed mirror is mounted at one end of this plate 
and is equipped with fine adjustment screws; the mov¬ 
able mirror is shown unattached. The metal plate is 
clamped across the bed plate of the micrometer slide, 
which is shown in Fig. 38. The micrometer screw of 
this slide has a pitch of 0.05 cm., and carries a head 
divided into 100 parts; thus movements of the carriage, 



Fig. 38. 


upon which is mounted the movable mirror (AT of 
Fig. 36), can be read to 0.00005 by estimating tenths 
of divisions on the micrometer head. A pinion shown 
at the bottom of Fig. 37 can be adjusted to engage 
the finely knurled edge of the micrometer head of Fig. 
38, so that the carriage may be given a slow motion. 

Procedure. Do not touch any optical surfaces of the 
apparatus. See that the interferometer attachment is 
firmly clamped to the bed plate of the micrometer slide. 
Then move the slide until the mirror on it is at a distance 
away from some reference point on the half-silvered 
surface s of plate A equal to the distance of the fixed 









112 PHYSICAL LABORATORY EXPERIMENTS 


mirror from that same point. This adjustment may be 
effected by means of dividers or with the aid of the 
mm. scale on the micrometer slide. Place the sodium 
burner near the principal focus of a short-focus lens and 
allow the resulting parallel beam of yellow light to fall 
upon plate A. While looking into the instrument from 
0, Fig. 36, shift the lens or burner to such position as 
will yield uniform illumination of the entire surface of 
plate A. Now hold a pin between this plate and the 
lens and three images will be observed, the third image 
being introduced by reflection from plate A at its un¬ 
silvered side. To eliminate the odd image, alter the 
inclination of mirror M by its adjusting screws until 
a coincidence is established between this image and 
either one of the other two. 

When properly adjusted, there will be visible from 0, 
across mirror M, a series of bands, called interference 
fringes, which represent the intersection of that mirror 
with a series of interference planes. These fringes are 
to be found by moving the eye sidewise and to and 
from plate A. If not directly visible, carefully adjust 
the screws at mirror M and search for the fringes. When 
they have been located, again adjust the position of 
mirror M so that the fringes will be vertical and that 
about a half dozen will be simultaneously in view. As 
the micrometer slide is moved slowly in either direction, 
these fringes will progress across the field of view, a 
movement of one fringe to the next corresponding to 
an advance on the part of the movable mirror of one- 
half wave-length of the light under investigation. 

Observations and Conclusions. Focus the observ¬ 
ing telescope on the fringes and note the position of the 
movable mirror by reading the mm. scale and the divi¬ 
sions on the micrometer head. Turn the micrometer screw 
slowly by means of the pinion head until 200 fringes have 
passed the vertical cross-hair of the telescope and 
again note the position of the movable mirror. Repeat 
this process until 1000 fringes in all have been counted. 


PHYSICAL LABORATORY EXPERIMENTS 113 


If l cm. be the distance moved by the carriage support¬ 
ing the movable mirror for the passage of 1000 fringes, 
then the wave-length of yellow light is X = Z/500 cm. 
Compare this result with the value given in Table XIV. 

EXPERIMENT 29 
Wave-lengths of Light by Diffraction 

Object. To measure the wave-length of several 
colored lights by means of a reflection diffraction grating. 

Theory. The reflection grating consists of a large 
number of parallel reflecting metal 
strips separated by narrow non-reflect¬ 
ing spaces. The action of such a 
grating is illustrated in Fig. 39, in 
which the lines a , b, c, d and e repre¬ 
sent horizontal sections of successive 
vertical reflecting strips, I shows an 
incident plane wave-front of mono¬ 
chromatic light striking the plane of 
the grating at an angle i, D repre¬ 
sents the first-order diffracted wave- 
front, making an angle 8 with the 
grating, and s is the distance between 
successive centers of the reflecting 
strips. For the first-order diffracted 
wave-front shown at D, the distance 
p -f- q is one wave-length or X, but in general, for the 
nth-order diffracted wave-front 

p + q = nX. 

Consequently from the figure 

s sin i + s sin 8 = nX, 
whence the wave-length is 

X = - ( sin i + sin 8 ). 
n 



114 PHYSICAL LABORATORY EXPERIMENTS 


When the incident beam is normal to the surface of the 
grating it follows that sin i = 0 in the expression for X. 
Further, sin 8 may be expressed in terms of l and m; 
consequently the wave-length of that color whose fringe 
is m cm. from the zero mark of the scale, is 

ms 

X = —t=. 
nVl 2 + m 2 

Apparatus. Speculum-metal diffraction grating, arc 
or incandescent-lamp projection lantern with optical 
bench, slit of adjustable width, and two cm. scales. 

The grating to be used has 14,438 reflecting strips per 
inch, therefore the distance between successive strips 
is 0.00017592 cm. Do not touch the surface of the 
grating. 

Procedure. Place the arc light or the concentrated- 
filament lamp at the principal focus of the condensing 
lens of the projection lantern. Clamp the slit on the 
optical bench near the condensing lens, and place the 
projection lens some distance in front of the slit. Place 
the grating in front of the projection lens so that the 
reflecting strips are very slightly inclined to the vertical 
and that the normal to the grating surface and the lens 
axis lie in the same vertical plane. Mount the straight 
scale in a horizontal position just above and perpendicular 
to the axis of the projecting lens, with the zero mark 
of the scale vertically above this axis. Illuminate the 
arc or lamp, and adjust the positions of the grating, lens 
and scale until a clearly defined white image of the slit 
is formed by reflection at the zero mark of the scale. 
If the slit be made quite narrow, the diffracted rays will 
be seen as continuous spectra on both sides of the reflected 
image. 

Observations. When the parts are in proper adjust¬ 
ment, note the distance m of the violet, green, yellow and 
red fringes from the zero mark of the scale and meas¬ 
ure the perpendicular distance l of the grating from the 
scale. If the scale extends only to one side of the lens 




PHYSICAL LABORATORY EXPERIMENTS 115 


the grating may be turned 180° around the normal 
to its surface in order to take observations of the other 
spectral image. Readjust the apparatus and take 
another set of readings. 

Conclusions. Compute the wave-lengths of the colors 
mentioned above from readings on the first-order spectral 
images. Express the results also in microns (1 micron 
= 0.001 mm. = ju). Refer to Table XIY. 


EXPERIMENT 30 

Photometric Test of Incandescent Lamp 

Object. To determine the candle-power of a tungsten- 
jlament lamp at various angles in a plane through the 
tip and base of the lamp with the Lummer-Brodhun 
contrast photometer. The results are plotted in polar 
coordinates to form a light-distribution curve, from 
which the mean candle-power in that plane may be 
determined. 

Theory. The lamp to be tested and the standard 
lamp are clamped at opposite ends of an optical bench 
and between them is a movable opaque white screen, 
both sides of which may be viewed simultaneously by 
an optical arrangement. The position of the screen 
is altered until the illumination of both sides of the 
screen is identical. If, after this adjustment, the dis¬ 
tance of the lamp under test of candle-power 7, from the 
screen be Z, and the distance of the standard lamp of 
candle-power I s from the screen be l s , then since the 
intensity of illumination varies inversely as the square 
of the distance from the light source, it follows that the 
illumination of the photometer screen is 



116 PHYSICAL LABORATORY EXPERIMENTS 


As the distance L between the lamps remains unchanged, 
the candle-power of the lamp under test may be ex¬ 
pressed as 



If the candle-power of a lamp be measured at various 
angles in a plane through its tip and base, these values 
when plotted on polar coordinate paper would form the 
light-distribution curve of the lamp in that plane. Had 
the lamp been rotated about its own axis during the 
candle-power measurements the resulting distribution 
curve would be the average for every plane containing 
the lamp axis. A distribution curve shows that the 
intensity of illumination from a lamp is not the same 
in all directions, therefore for purposes of comparison 
it is desirable to determine the mean spherical candle- 
power of the lamp. This cannot be obtained by merely 
averaging the candle-powers of the lamp as measured 
at equal angular intervals because of the wide differ¬ 
ence in the corresponding zonal areas. It has been 
computed that the angles measured from the lamp axis 
at which values may be read from a light-distribution 
curve and directly averaged in order to obtain the mean 
spherical candle-power are: 24, 41, 54, 65, 75, 85, 95, 
105, 115, 126, 139, and 156 degrees (see Standard Hand¬ 
book for Electrical Engineers, ed. 4, p. 1138). 

Apparatus. Two-meter photometer bench with three 
carriages for supporting screen and lamps, Lummer- 
Brodhun photometer head, standardized tungsten filament 
lamp, lamp to be tested, slide-wire rheostat, and volt¬ 
meter. 

The Lummer-Brodhun photometer head is illustrated 
in Fig. 40. 

The screen S has its two sides illuminated by the light 
sources L x and L 2 , and these surfaces may be viewed 
simultaneously by means of the mirrors M x and M 2 , the 
right-angled prisms P x and P 2 , and the telescope. The 



PHYSICAL LABORATORY EXPERIMENTS 117 


prisms are ground so that the actual surface of contact 
between the two prisms has the shape indicated by the 
unshaded part of F, while the shaded part shows where 
a narrow layer of air separates the prisms. Light from 
the right side of screen S after reflection from mirror Mi 
enters prism Pi normally, and that part which strikes the 
junction surface in the places where the two prisms are 
not in contact is totally reflected out of the prism and 



into the telescope, while the remaining portion of the 
entering light strikes the contact surface and is trans¬ 
mitted directly through prism P 2 to R. Similarly a 
part of the light from the other side of the screen is trans¬ 
mitted to the telescope while the remainder is totally 
reflected to R . The cross-sections of the beams of light 
entering the telescope will then resemble the configurator 
shown at F, wherein the shaded parts depict the cross- 
sections of the beams from the right side of S, and the 
unshaded parts show the beams from the left side of the 




















118 PHYSICAL LABORATORY EXPERIMENTS 

screen. Thus each of the two light sources illuminates 
a trapezoidal-shaped figure within a semicircular field 
that is illuminated by the other source. The rays of 
light from the two sides of the screen which illuminate 
the trapezoids are shown by the dotted lines in the figure. 
Both trapezoids are made a few per cent darker than their 
corresponding opposite semicircular fields by the inter¬ 
position of the thin glass plates Gi and G 2 , which absorb 
a small amount of the light going to the trapezoids. 

To take a reading with the Lummer-Brodhun photom¬ 
eter, the screen is moved to such a position between 
the two light sources that the two trapezoids are both 
darker than the surrounding semicircular fields and 
the contrasts between each trapezoid and its surround¬ 
ing field are identical. When the two sources are of 
exactly the same color the dividing line between the two 
semicircular fields will disappear when the screen is prop¬ 
erly located. 

Procedure and Observations. Place the standard 
lamp in its socket at the center of the carriage table 
so that the mark etched on its bulb is directed toward 
the photometer screen. Place the lamp to be tested in 
the socket on the swivel arm of the other carriage, and 
turn the arm till its associated graduated disk indicates 
0 degrees against its stationary index. Move the two 
lamp carriages to the ends of the photometer bench and 
clamp the standard lamp at the zero mark and the lamp 
under test at the 200 mark of the cm. scale engraved 
on the photometer bench. Adjust the heights of the 
lamps and the screen so that the centers of the filaments 
and of the screen lie in one horizontal line. The lamps 
are connected in parallel to the electricity mains through 
a common regulating rheostat and a voltmeter is bridged 
across the lamps. Illuminate the lamps and adjust the 
voltage across them to the value marked on the lamp 
under test. Move the screen to such position on the 
bench between the lamps that will yield equal contrasts 
between the two trapezoidal-shaped figures and their 


PHYSICAL LABORATORY EXPERIMENTS 119 


surrounding semicircular fields. Be sure that the tele¬ 
scope is properly focused on the trapezoids before 
making settings of the screen. Note the position of the 
screen carriage. To avoid errors due to dissymmetry 
in the photometer head, reverse the head, readjust for 
equality of contrast and record the position of the screen. 

Then move the arm carrying the test lamp 20 degrees 
from its former position and take readings of the screen 
positions. Repeat this procedure at intervals of 20 
degrees until the lamp again reaches its initial position. 
Arrange all observations in tabular form. Turn out the 
standard lamp immediately after all readings have been 
taken. 

Conclusions. The mean reading l s for the two set¬ 
tings of the screen made at each angular position of the 
test lamp is obtained by taking the square root of the 
product of the two observations, but if the difference 
of the settings is small, the arithmetical mean of the 
observations is sufficiently accurate. Determine the 
candle-power I s of the standardized lamp at the voltage 
employed from its calibration curve. Compute the can¬ 
dle-power of the test lamp for each position and plot 
the results on polar coordinate paper. Sketch the posi¬ 
tion of the lamp around the origin and indicate the scale 
of candle-power along a single diameter. From this 
distribution curve determine the mean spherical candle- 
power of the lamp tested. 




APPENDIX 


TABLES OF PHYSICAL 
CONSTANTS 



















































































































































TABLES OF PHYSICAL CONSTANTS 


123 


Table I 

AND CONVERSION FACTORS 
c = 2.7183 

log € 10 = 1 = 2.3026 

logio e 

1 radian = 57.2958 degrees 
1 degree = 0.017453 radian 


CONSTANTS 

t r = 3.1416 
7T 2 = 9.8696 

- = 0.31831 

logxoTr = 0.49715 

1 micron = M = 0.001 mm. 

1 centimeter = 0.39370 inch 
1 inch = 2.5400 cm. 

1 foot = 30.480 cm. 

1 meter = 3.2808 feet 
1 kilometer = 0.62137 mile 
1 mile = 1.6094 km. 


1 sq. inch = 6.4516 sq. cm. 

1 sq. foot = 929.03 sq. cm. 

1 sq. meter = 10.764 sq. feet 
1 cu. inch = 16.387 cu. cm. 

1 liter = 1000 cu. cm. 

1 gallon = 3.7853 liters 
1 cu. foot = 0.028317 cu. meter 


1 gram = 15.432 grains 1 pound = 453.59 grams 

1 ounce = 28.350 grams 1 kilogram = 2.2046 pounds 

1 hour = 3600 seconds 1 mean solar year = 8766 hours 

1 sidereal year = 365 days, 6 hours, 9 minutes, 9.314 seconds 

1 pound (wt.) = 444,790 dynes* 1 foot-pound = 1.3549 joules 
1 bar = pressure of 0.00075 mm. Hg. 

1 gram per sq. cm. = 0.01422 pound per sq. inch 
1 pound per sq. inch = 70.307 grams per sq. cm. 

1 atmosphere pressure = 14.697 pounds per sq. inch 
1 joule = 10,000,000 ergs 1 B.T.U. = 252.00 calories 

1 calorie = 4.186 joules 1 B.T.U. = 778.07 foot-pounds* 

1 calorie = 0.42688 kg-meters* 1 horse power = 746 wattsf 

* For g = 980.6 (45° latitude). t For g = 981.2 (at London). 


Table II 

ACCELERATION OF GRAVITY 


Place 

Q 

cm./sec. 2 

Place 

g 

cm./sec. 2 

Berlin, Germany. . . . 

Boston, Mass. 

Chicago, Ill. 

Denver, Colo. 

London, England.. . . 

Madison, Wis. 

New Orleans, La. 

981.276 
980.362 
980.274 
979.628 
981.194 
980.352 
979.313 

New York, N. Y. 

Paris, France. 

Philadelphia, Pa. 

Rome, Italy. 

St. Louis, Mo. 

San Francisco, Cal. . 
Washington, D. C. . . 

980.225 
980.943 
980.138 
980.316 
979.993 
979.935 
980.050 


The value of g at any latitude X and at any altitude h meters may be com¬ 
puted from the equation: 

g = 980.616 (1 - 0.00266 cos 2X - 0.00000020 h). 




























124 


APPENDIX 


Table III 

HARDNESS OF METALS 


(Shore Scleroscope Scale) 


Metal 

Annealed 

Hammered 

Rabbi tt. 

4-9 


Rismuth (oast). 

9 


Rrass (oast). 

7-35 


Brass (drawn). 

10-15 

20-45 

Copper (cast). 

6 

14-20 

Gold. 

5 

8-9 

Iron, pure. 

18 

25-30 

Iron, gray (cast). 

Iron errav (chilled). 

30-45 

50-90 

Lead (cast). 

2-5 

3-7 

Phosphor bronze . 

20 

35 

Platinum. 

10 

17 

Silver . 

6-7 

20-30 

Steel carbon tool (hardened). 


90-110 

Steel chrome-nickel. 

47 

Steel, chrome-nickel (hardened). 

Steel, high-speed (hardened). 

Steel, mild, 0.15% carbon. 

Steel tool 1.0% carbon. 

22 

30-35 

60-° r » 
70-105 
30-45 
40-50 

Steel, tool, 1.65% carbon. 

Steel, vanadium. 

35-40 

35-45 

Tin, pure (cast). 

8 

12 

Zinc (cast). 

8 

20 



These figures, given by th3 Share Instrument and Mfg. Co., are subject to 
variations owing to nature of composition or compression of metals. 


Table IV 


COEFFICIENTS OF ELASTICITY 


Substance 

Stretch Modulus 

Shear Modulus 

10 11 dynes 
per sq. cm. 

10® pounds 
per sq. in. 

10 11 dynes 
per sq. cm. 

10® pounds 
per sq. in. 

Aluminum.. . . 
Brass. 

7.1- 7.3 
8.4-10.2 
10.3-12.9 
6.0- 8.0 
11.5 

19.0-21.3 

17.0-21.3 

10.3-10.6 

12.2-14.8 

15.0-18.7 

8.7-11.6 

16.7 

27.5-31.0 

24.7-31.0 

2.5- 3.3 

2.6- 3.6 

3.8-4.5 

2.3- 2.7 

} 5.1-8.3 

7.3- 8.4 

3.6- 4.8 
3.8- 5.2 
5.5- 6.5 

3.3- 3.9 

7.4- 12.0 

10.6-12.2 

Copper. 

Glass. 

Iron (cast).. . . 
Iron (drawn).. 
Steel. 


















































TABLES OF PHYSICAL CONSTANTS 


125 


Table V 


VISCOSITIES OF LIQUIDS 


Liquid. 

Temperature 
° C. 

Coefficient of 
Viscosity 
dynes per sq. cm. 

Alcohol (ethyl). 

Alcohol (ethyl). 

0 

20 

10 

2.8 

20.3 

20 

15 

17.5 

0 

0.0177 
n ni i q 

Ether. 

u.ui iy 

Glycerine. 

u.uuzo 

49 9/1 

Glycerine. 

8.30 
/i m 

Mercury. 

Olive oil. 

U.UlOi 

0 QQQ 

Petroleum. 

u. yoy 
n m on 

Water. 

u.uiyu 
n ni7Q 


u.ui /y 


SPECIFIC VISCOSITY OF WATER 


Temper¬ 
ature 0 C. 

Viscosity 

0 

1.000 

5 

0.849 

10 

730 

15 

637 

20 

561 

25 

498 

30 

446 


Temper¬ 
ature ° C. 

Viscosity 

35 

0.404 

40 

367 

45 

335 

50 

307 

55 

283 

60 

262 

65 

243 


Temper¬ 
ature ° C. 

Viscosity 

70 

0.226 

75 

212 

80 

199 

85 

187 

90 

176 

95 

167 

100 

158 


Table VI 

DENSITY AND COEFFICIENTS OF EXPANSION OF 
GASES 


(At 76 cm. Hg.) 


Gas 

Density 
grams per 
liter at 0° C. 

Pressure 
Coefficient 
at constant volume 
(bet. 0 and 100° C) 

Coefficient of 
Cubical Expansion 
at constant pres¬ 
sure 

(bet. 0 and 100° C) 

Air. 

1.2928 

0.003665 

0.003671 

Carbon dioxide.. . 

1.9768 

0.003706 

0.003710 

Chlorine. 

3.1674 

0.003807 

0.003833 

Hydrogen. 

0.0900 

0.003656 

0.003661 

Nitrogen. 

1.2514 

, 0.003668 

0.003671 

Oxygen. 

1.4292 

0.003668 

0.003674 















































126 


APPENDIX 


Table VII 

SPECIFIC HEATS OF GASES 


Gas 

Specific Heat 
at constant 
pressure 

Ratio of Specific 
Heat at constant 
pressure to that at 
constant volume 

Air. 

0.238 

1.403 

Carbon dioxide 


0.203 

1.300 

Chlorine. 


0.124 

1.33 

1.408 

Hydrogen. 

3.405 

Nitrogen. 

0.244 

1.414 

Oxviren. 

0.218 

1.398 

Steam (at 100° 

C.).. 

0.421 

1.33 



Table VIII 

DENSITY AND SPECIFIC HEATS OF SOLIDS AND LIQUIDS 
At Ordinary Temperatures 


Substance 


Density gr./cu.cm. 


Specific Heat 


Alcohol, ethyl (0° C.)- 

Aluminum. 

Antimony. 

Bismuth. 

Brass. 

Carbon bisulphide (0° C.) 

Copper. 

German silver. 

Glass. 

Glycerine. 

Iron (wrought).. .. 

Lead. 

Marble. 

Mercury (0° C.). 

Nickel. 

Platinum. 

Silver. 

Steel. 

Sugar. 

Tin.,. 

Turpentine (10° C.). 

Vulcanite. 

Water (4° C.). 

Zinc. ,. 


0.81 

0.55 

2.6- 2.8 

0.212 

6.2- 6.7 

0.050 

9.7- 9.9 

0.030 

8.2- 8.7 

0.088-0.095 

1.29 

0.235 

8.4- 8.9 

0.093 

8.3- 8.8 

0.095 

2.4- 6.3 

0.11-0.20 

1.27 

0.576 

7.8- 7.9 

0.115 

11.3-11.4 

0.031 

2.6- 2.8 

0.21 

13.596 

0.0334 

8.6- 8.9 

0.113 

21.4 

0.032 

10.4-10.6 

0.056 

7.6-7.8 

0.117 

1.61 

0.304 

7.0- 7.3 

0.055 

0.87 

0.43 

1.2 

0.331 

1.000 

1.003 

6.9- 7.2 

0.093 














































TABLES OF PHYSICAL CONSTANTS 127 
Table IX 

LOCAL GEOGRAPHICAL DATA— Brooklyn, N. Y. 


Latitude of Polytechnic Institute. 40° 41' 33" 

Longitude of Polytechnic Institute. 73° 59' 28" West 

Altitude of Physical Laboratory fljor above mean 

sea level. 23.386 meters 

Value of g in Physical Laboratory. 980.220 cm/sec 2 


Table X 


HEATS OF FUSION AND VAPORIZATION 


Substance 

Melting- 
point 
° C. 

Heat of 
Fusion 
cal./gram 

Boiling- 

pcint 

° c. 

Heat of 
Vaporization 
cal./gram 

Alcohol (ethyl).. . . 

-130 


78.4 

205 

Benzol. 

5.6 

30.6 

80.2 

93.5 

Bismuth. 

270 

12.6 

1430 


Bromine. 

-7.3 

16.2 

61 

45.6 

Carbon bisulphide. 

-110 


46.2 

83.8 

Ether (ethyl). 

-118 


34.6 

90 

Lead. 

326 

5.4 

1525 


Mercury. 

-38.7 

2.8 

357 

65 

Paraffin. 

52 

35.1 

390 


Platinum. 

1755 

27.2 



Sulphur. 

115 

9.4 

444.7 


Water. 

0 

79.9 

100 

535.9 

Zinc. 

419 

28.1 

930 



Table XI 

HEATS OF COMBUSTION 


Substance 

Calories per 
gram 

Acetylene. 

11900 

Alcohol (ethyl).. . . 

7200 

Coal (American).. . 

6500- 8300 

Coal gas. 

5800-11000 

Dynamite (75%).. 

1290 


Substance 

Calories per 
gram . 

Hydrogen. 

34000 

Illuminating gas. . 

5200-6000 

Petroleum. 

11000 

Sulphur. 

2200 

Woods (various). . 

4000-4900 
















































APPENDIX 


128 


Table XII 


PRESSURE OF WATER VAPOR (Saturated) 
(Inches of Hg.) 


Temper¬ 
ature ° F. 

Vapor 

Pressure 

Temper¬ 
ature 0 F. 

Vapor 

Pressure 

Temper¬ 
ature ° F. 

Vapor 

Pressure 

0 

0.0383 

34 

0.195 

68 

0.684 

1 

403 

35 

203 

69 

707 

2 

423 

36 

211 

70 

732 

3 

444 

37 

219 

71 

757 

4 

467 

38 

228 

72 

783 

5 

491 

39 

237 

73 

810 

6 

515 

40 

247 

74 

838 

7 

542 

41 

256 

75 

866 

8 

570 

42 

266 

76 

896 

9 

600 

43 

277 

77 

926 

10 

631 

44 

287 

78 

957 

11 

665 

45 

298 

79 

989 

12 

699 

46 

310 

80 

1.022 

13 

735 

47 

322 

81 

056 

14 

772 

48 

334 

82 

091 

15 

810 

49 

347 

83 

127 

16 

850 

50 

360 

84 

163 

17 

891 

51 

373 

85 

201 

18 

933 

52 

387 

86 

241 

19 

979 

53 

402 

87 

281 

20 

0.1026 

54 

417 

88 

322 

21 

108 

55 

432 

89 

364 

22 

113 

56 

448 

90 

408 

23 

118 

57 

465 

91 

453 

24 

124 

58 

482 

92 

499 

25 

130 

59 

499 

93 

546 

26 

136 

60 

517 

94 

595 

27 

143 

61 

536 

95 

645 

28 

150 

62 

555 

96 

696 

29 

157 

63 

575 

97 

749 

30 

164 

64 

595 

98 

803 

31 

172 

65 

616 

99 

859 

32 

180 

66 

638 

100 

916 

33 

187 

67 

661 

101 

975 































TABLES OF PHYSICAL CONSTANTS 


129 


Table XIII 


THERMAL CONDUCTIVITY 


Substance 

Temperature 
0 C. 

Conductivity 
calories per cm. per 
sec. per ° C. 

Air. 

0 

0.000046-0.000057 

Aluminum. 

18 

0.48 

Copper (pure). 

20 

0.89-0.95 

Flannel. 

50 ; 

0.000036 

Glass. 

15 

0.0011-0.0023 

Iron (wrought). 

20 

0.15-0.21 

Marble. 

30 

0.0060 

Mercury. 

50 

0.018 

Silver. 

18 

1.006 

Water . 

1C 

0.0013 


Table XIV 

INDICES OF REFRACTION 


. Solar Line 

B 

C 

D 

E 

F 

G 

H 

Substance 

O 

H 

Na 

Ca 

H 

Fe, Ca 

H, Ca 

Wave-length (/i) 

0.6870 

0.6563 

0.5893 

0.5270 

0.4862 

0.4308 

0.3969 

Color 

red 

red 

yellow 

green 

blue 

violet 

violet 

Alcohol (15° C.). 

1.3599 

1.3606 

1.3624 

1.3647 

1.3667 

1.3705 

1.3736 

Carbon bisulphide (20° C.). 

1.6150 

1.6185 

1.6277 

1.6407 

1.6526 

1.6767 

1.7001 

Crown glass (8 = 2.5). 

1.5118 

1.5127 

1.5153 

1.5186 

1.5214 

1.5267 

1.5312 

Flint glass (8 = 4.7). 

1.7406 

1.7434 

1.7515 

1.7623 

1.7723 

1.7922 

1.8110 

Water (20° C.). 

1.3309 

1.3311 

1.3330 

1.3352 

1.3372 

1.3412 

1.3435 


Accepted primary wave-length standard is that of the red cadmium line in 
air (76 cm. Hg. and 15° C.): 0.000064384606 cm. 


Table XV 

CONSTANTS OF THE NORMAL HUMAN EYE 


Part of Eye 

Radii of Curvature 
cm. 

Thickness 

cm. 

Index 

of 

Re¬ 

fraction 

Front Surface 

Rear Surface 

Cbrnea.. .. 

Aqueous humor. 

Crystalline lens. 

Vitreous humor. 

+0.783 

+0.733 

+ 1.00 (+0.60) 
-0.60 (-0.55) 

-0.733 

-1.00 (-0.60) 
+0.60 (+0.55) 
+ 1.2 

0.05-0.06 
0.36 (0.32) 
0.36 (0.40) 
1.59 

1.351 

1.337 

1.437 

1.337 


The values in the parentheses are applicable to the accommodated eye. 






























































130 


APPENDIX 


Table XVI 
VELOCITY OF SOUND 


Substance 

Temperature 
3 C. 

Velocity 
meters per sec. 

Air. 

0 

12.5 

331.7 

1241 

Alcohol. 

Aluminum. 

15 

5100 

Brass'. 

15 

3500 

Copper. 

20 

3560 

Glass. 

15 

5000-6000 

Hydrogen. 

0 

1286.4 

Illuminating gas. 

0 

490.4 

Iron. 

20 

5130 

Oxygen.. 

0 

317.2 

Water. 

13 

1441 

Woods (various). 


1000-4700 




















INDEX 


(The figures refer 

Acceleration, angular, 23 

of gravity by Atwood’s ma¬ 
chine, 11 

by falling body, 14 
table of, 123, 127 
Air, conformity with Boyle’s 
law, 43 

thermometer, 57 
velocity of sound in, 50 
Amsler planimeter, 6 
Aneroid barometer, 43 
Angle of glass prism, 84 
Aqueous vapor, tension of, 128 
Areas, by planimeter, 6 
Astigmatism of eye, 94 
Atmosphere, dew-point of, 78 
humidity of, 78 
Atwood’s machine, 12 

Barometer, aneroid, 43 
Bi-refringent telescope, 96 
Boyle’s law, 43 

Bulk modulus of elasticity of 
gases, 51 

Bunsen ice calorimeter, 71 

Calibration of ocular cathetom- 
eter scale, 92 
of Venturi meter, 48 
Caliper, micrometer, 2 
vernier, 3 


to page numbers.) 

Callendar’s apparatus for heat 
equivalent of work, 69 
Calorimeter, Bunsen ice, 71 
Junker’s gas, 76 
Candle-power of lamp, 115 
Cathetometer, 93 
Coefficient of elasticity, 30, 33 
table of, 124 
expansion of gases, 57 
table of, 125 
restitution, 17 
rigidity, 33 
viscosity, 38 
Combustion, heat of, 74 
table of, 127 

Conductivity of metals for heat, 
82 

heat, table of, 129 
Constants, numerical, 123 
Conversion factors, 123 
Corneal astigmatism, 94 
Coulomb’s method for viscosity, 
38 

Current curve, area of, 10 
Curvature of cornea, 94, 129 
lenses, 1 
mirrors, 88 

Damped harmonic motion, 39 
Daniell hygrometer, 78 
Density of atmosphere, 50 



132 


INDEX 


Density of gases at different tem¬ 
peratures, 54 
by effusiometer, 45 
table of, 125 
liquids and solids, 126 
Dew-point of atmosphere, 78 
Diffraction grating, 113 
Diopter, definition of, 100 

Effusiometer, 45 
Elasticity, modulus of, 30, 33, 
51 

Electrical energy, heat equiva¬ 
lent of, 65 

Ewing’s extensometer, 31 
Expansion of gases, 57 
table of coefficients of, 125 
Extensometer, 31 
Eye, constants of, 129 
corneal astigmatism of, 94 

Falling body for measuring ac¬ 
celeration, 14 

Focal length of aqueous humor, 
100 

lenses, 88 

Fuels, heat of combustion of, 
74 

Fusion, heat of, 71 
table of, 127 

Gases, elasticity of, 51 
expansion of, 57 
table of, 125 
rate of flow, 47 
specific gravity of, 45 
heats of, 50 

velocity of sound in, 51 
Geographical data, local, 127 
Glass prism, refractive index of, 
84 

Grating, diffraction, 113 


Gravity with Atwood’s machine, 
11 

falling body, 14 

Hardness by scleroscope, 17 
of metals, table of, 124 
Harmonic motion, damped, 39 
rotatory, 26 

Heat equivalent of electrical 
energy, 65 

mechanical energy, 68 
of combustion of fuels, 74 
table of, 127 
of fusion of ice, 71 
table of, 127 
Hooke’s law, 30 
Humidity of atmosphere, 78 
Hygrodeik, 80 
Hygrometer, 78 
Hysteresis loop, area of, 10 

Ice calorimeter, 71 
Incandescent lamp, photometry 
of, 115 

Index of refraction of prism, 84 
Indicator diagram, area of, 10 
Indices of refraction, table of, 
129 

Inertia of oscillating body, mo¬ 
ment of, 26 

of wheel, moment of, 22 
Interferometer, 109 

Javal-Schiotz ophthalmometer, 
97 

Junker’s gas calorimeter, 76 

Ivundt’s tube, 55 

Laplace’s equation for velocity 
of sound, 52 

Least count of vernier, 4 




INDEX 


133 


Lenses, curvature of, 1 
focal lengths of, 88 
Light, wave-lengths of, 109, 113, 
129 

Liquids, density of, 126 
rate of flow, 48 
specific heats of, 126 
viscosity of, 38, 125 
Lummer-Brodhun photometer, 
116 

Magnifying power of microscope, 
102 

Mechanical equivalent of heat, 
65, 68 

Metals, elasticity of, 30, 33 
hardness of, 19 
table of, 124 
heat conductivity of, 82 
specific heats of, 62 
velocity of sound in, 50 
Michelson interferometer, 109 
Micrometer caliper, 2 
slide, 111 

Microscope, magnifying power 
of, 102 

ocular scale, calibration of, 92 
Minimum deviation of prism, 85 
Mirrors, curvature of, 88 
Mixtures, method of, 62 
Modulus of bulk elasticity, 51 
of shear, 33 
Young’s, 30 

Moment of inertia of oscillating 
body, 26 
of wheel, 22 

Motion, harmonic rotatory, 26 
laws of accelerated, 11 

Numerical constants, 123 

Ophthalmometer, 94 


Photometer, 116 
Photometric test of lamp, 115 
Planimeter, 6 
Psychrometer, 78 

Radiation, correction for, 66 
Radius of curvature of cornea, 
94, 129 
lenses, 1 
mirrors, 88 

Refractive index of prism, 84 
indices, table of, 129 
Restitution, coefficient of, 17 
Rigidity, modulus of, 33 
Rotatory harmonic motion, 26 

Scleroscope, 18 

Searle’s heat conductivity appa¬ 
ratus, 82 

Shear modulus of elasticity, 33 
Shore scleroscope, 17 
Slide modulus of elasticity, 33 
Sodium burner, 87 
Sound, velocity of, 50 
table of, 130 

Specific gravity of gases, 45 
heats of gases, 50 
table of, 126 
liquids, table of, 126 
solids, 62 
table of, 126 
viscosity of liquids, 38 
table of, 125 
Spectrometer, 86 
Speed-time curve, area of, 10 
Spherical candle-power, 116 
Spherometer, 2 
Steam, temperature of, 58 
Steel, hardness of, 21 
Stretch modulus of elasticity, 30 


J Thermometer, air, 57 




134 


INDEX 


Thermometer, mercury, correc¬ 
tions for, 63 

Torque, equations for, 22, 26 

Vaporization, table of heats of, 
127 

Velocity of sound, 50 
table of, 130 
Venturi meter, 48 
Vernier caliper, 3 
theory of, 4 
Viscosimeter, 41 
Viscosity of liquids, 38 


Viscosity, table of, 125 

Water equivalent of calorimeter, 
64 

specific viscosity of, 41 
vapor, table of pressures of, 
128 

Wave-lengths of light by dif¬ 
fraction, 113 
by interferometer, 109 
Wheel, moment of inertia of, 22 

Young’s elastic modulus, 26 





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